Category: Set theory

Silver's dichotomy
In descriptive set theory, a branch of mathematics, Silver's dichotomy is a statement about equivalence relations, named after Jack Silver.
Theories of iterated inductive definitions
In set theory and logic, Buchholz's ID hierarchy is a hierarchy of subsystems of first-order arithmetic. The systems/theories are referred to as "the formal theories of ν-times iterated inductive defi
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or
In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure . Jus
Hereditarily finite set
In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements ar
Subclass (set theory)
In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained in some other set. That is, given classe
List of set theory topics
This page is a list of articles related to set theory.
Set intersection oracle
A set intersection oracle (SIO) is a data structure which represents a collection of sets and can quickly answer queries about whether the set intersection of two given sets is non-empty. The input to
Preordered class
In mathematics, a preordered class is a class equipped with a preorder.
Implementation of mathematics in set theory
This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theor
Conglomerate (mathematics)
In mathematics, in the framework of one-universe foundation for category theory, the term "conglomerate" is applied to arbitrary sets as a contraposition to the distinguished sets that are elements of
Solovay model
In the mathematical field of set theory, the Solovay model is a model constructed by Robert M. Solovay in which all of the axioms of Zermelo–Fraenkel set theory (ZF) hold, exclusive of the axiom of ch
Hereditary property
In mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly co
Primitive recursive set function
In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They
Total order
In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and
Mostowski model
In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by Mostowski. The Mos
Tarski's theorem about choice
In mathematics, Tarski's theorem, proved by Alfred Tarski, states that in ZF the theorem "For every infinite set , there is a bijective map between the sets and " implies the axiom of choice. The oppo
Stratification (mathematics)
Stratification has several usages in mathematics.
Hausdorff Medal
The Hausdorff medal is a mathematical prize awarded every two years by the European Set Theory Society. The award recognises the work considered to have had the most impact within set theory among all
Tree (set theory)
In set theory, a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. mi
Successor cardinal
In set theory, one can define a successor operation on cardinal numbers in a similar way to the successor operation on the ordinal numbers. The cardinal successor coincides with the ordinal successor
Infinitary combinatorics
In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets.Some of the things studied include continuous graphs and trees, extens
Lévy hierarchy
In set theory and mathematical logic, the Lévy hierarchy, introduced by Azriel Lévy in 1965, is a hierarchy of formulas in the formal language of the Zermelo–Fraenkel set theory, which is typically ca
List of set identities and relations
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It
Equivalence class
In mathematics, when the elements of some set have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set into equivalence classes. These equivalence cla
Club set
In mathematics, particularly in mathematical logic and set theory, a club set is a subset of a limit ordinal that is closed under the order topology, and is unbounded (see below) relative to the limit
Cardinal assignment
In set theory, the concept of cardinality is significantly developable without recourse to actually defining cardinal numbers as objects in the theory itself (this is in fact a viewpoint taken by Freg
Null set
In mathematical analysis, a null set is a measurable set that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total leng
Chang's conjecture
In model theory, a branch of mathematical logic, Chang's conjecture, attributed to Chen Chung Chang by , p. 309), states that every model of type (ω2,ω1) for a countable language has an elementary sub
Club filter
In mathematics, particularly in set theory, if is a regular uncountable cardinal then , the filter of all sets containing a club subset of , is a -complete filter closed under diagonal intersection ca
Takeuti–Feferman–Buchholz ordinal
In the mathematical fields of set theory and proof theory, the Takeuti–Feferman–Buchholz ordinal (TFBO) is a large countable ordinal, which acts as the limit of the range of Buchholz's psi function an
Soft set
Soft set theory is a generalization of fuzzy set theory, that was proposed by Molodtsov in 1999 to deal with uncertainty in a parametric manner. A soft set is a parameterised family of sets - intuitiv
Structuralism (philosophy of mathematics)
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their pla
Suslin representation
In mathematics, a Suslin representation of a set of reals (more precisely, elements of Baire space) is a tree whose projection is that set of reals. More generally, a subset A of κω is λ-Suslin if the
Set-theoretic topology
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of Zermelo–Fraenkel set theory (ZFC).
In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A. This definition of cofinality relies on the
Transitive set
In set theory, a branch of mathematics, a set is called transitive if either of the following equivalent conditions hold: * whenever , and , then . * whenever , and is not an urelement, then is a su
Multiverse (set theory)
In mathematical set theory, the multiverse view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various models are all equally valid or true, though so
Hydra game
In mathematics, specifically in graph theory and number theory, a hydra game is a single-player iterative mathematical game played on a mathematical tree called a hydra where, usually, the goal is to
Hartogs number
In mathematics, specifically in axiomatic set theory, a Hartogs number is an ordinal number associated with a set. In particular, if X is any set, then the Hartogs number of X is the least ordinal α s
Closure (mathematics)
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the n
Continuum (set theory)
In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by . Georg Cantor proved that the cardinality is larger than the
Sierpiński set
In mathematics, a Sierpiński set is an uncountable subset of a real vector space whose intersection with every measure-zero set is countable. The existence of Sierpiński sets is independent of the axi
Supertransitive class
In set theory, a supertransitive class is a transitive class which includes as a subset the power set of each of its elements. Formally, let A be a transitive class. Then A is supertransitive if and o
Hume's principle
Hume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in
Deductive closure
In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the dedu
Paradoxes of the Infinite
Paradoxes of the Infinite (German title: Paradoxien des Unendlichen) is a mathematical work by Bernard Bolzano on the theory of sets. It was published by a friend and student, , in 1851, three years a
Theory of regions
The Theory of regions is an approach for synthesizing a Petri net from a transition system. As such, it aims at recovering concurrent, independent behavior from transitions between global states. Theo
Sunflower (mathematics)
In the mathematical fields of set theory and extremal combinatorics, a sunflower or -system is a collection of sets whose pairwise intersection is constant. This constant intersection is called the ke
Paradoxical set
In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is two families of disjoint subsets, along with appropriate group actions that act
Jónsson function
In mathematical set theory, an ω-Jónsson function for a set x of ordinals is a function with the property that, for any subset y of x with the same cardinality as x, the restriction of to is surjectiv
Diagonal intersection
Diagonal intersection is a term used in mathematics, especially in set theory. If is an ordinal number and is a sequence of subsets of , then the diagonal intersection, denoted by is defined to be Tha
Schröder–Bernstein property
A Schröder–Bernstein property is any mathematical property that matches the following pattern If, for some mathematical objects X and Y, both X is similar to a part of Y and Y is similar to a part of
Paradoxes of set theory
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logi
BIT predicate
In mathematics and computer science, the BIT predicate or Ackermann coding, sometimes written BIT(i, j), is a predicate that tests whether the jth bit of the number i is 1, when i is written in binary
Class logic
Class logic is a logic in its broad sense, whose objects are called classes. In a narrower sense, one speaks of a class logic only if classes are described by a property of their elements. This class
Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the mul
Hereditary set
In set theory, a hereditary set (or pure set) is a set whose elements are all hereditary sets. That is, all elements of the set are themselves sets, as are all elements of the elements, and so on.
PCF theory
PCF theory is the name of a mathematical theory, introduced by Saharon Shelah, that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of
Inhabited set
In constructive mathematics, a set is inhabited if there exists an element In classical mathematics, this is the same as the set being nonempty; however, this equivalence is not valid in intuitionisti
Pairing function
In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set theory to prove that integers and rational
Square principle
In mathematical set theory, a square principle is a combinatorial principle asserting the existence of a cohering sequence of short closed unbounded (club) sets so that no one (long) club set coheres
Categorical set theory
Categorical set theory is any one of several versions of set theory developed from or treated in the context of mathematical category theory.
Laver function
In set theory, a Laver function (or Laver diamond, named after its inventor, Richard Laver) is a function connected with supercompact cardinals.
The Mengenlehreuhr (German for "Set Theory Clock") or Berlin-Uhr ("Berlin Clock") is the first public clock in the world that tells the time by means of illuminated, coloured fields, for which it ente
Reflection principle
In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that resemble the class of all sets. There are several different forms of the reflection principle
Computable ordinal
In mathematics, specifically computability and set theory, an ordinal is said to be computable or recursive if there is a computable well-ordering of a subset of the natural numbers having the order t
Erdős–Rado theorem
In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to uncountable sets. It is named after Paul Erdős
Cantor's diagonal argument
In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, w
List of types of sets
Sets can be classified according to the properties they have.
In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends on the cont
Kuratowski's free set theorem
Kuratowski's free set theorem, named after Kazimierz Kuratowski, is a result of set theory, an area of mathematics. It is a result which has been largely forgotten for almost 50 years, but has been ap
Scott's trick
In set theory, Scott's trick is a method for giving a definition of equivalence classes for equivalence relations on a proper class (Jech 2003:65) by referring to levels of the cumulative hierarchy. T
Martin's axiom
In the mathematical field of set theory, Martin's axiom, introduced by Donald A. Martin and Robert M. Solovay, is a statement that is independent of the usual axioms of ZFC set theory. It is implied b
Nested set
In a naive set theory, a nested set is a set containing a chain of subsets, forming a hierarchical structure, like Russian dolls. It is used as reference-concept in all scientific hierarchy definition
Glossary of set theory
This is a glossary of set theory.
Named set theory
Named set theory is a branch of theoretical mathematics that studies the structures of names. The named set is a theoretical concept that generalizes the structure of a name described by Frege. Its ge
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as
Set theory of the real line
Set theory of the real line is an area of mathematics concerned with the application of set theory to aspects of the real numbers. For example, one knows that all countable sets of reals are null, i.e
Hausdorff gap
In mathematics, a Hausdorff gap consists roughly of two collections of sequences of integers, such that there is no sequence lying between the two collections. The first example was found by Hausdorff
List of statements independent of ZFC
The mathematical statements discussed below are provably independent of ZFC (the canonical axiomatic set theory of contemporary mathematics, consisting of the Zermelo–Fraenkel axioms plus the axiom of
In mathematics, a pantachy or pantachie (from the Greek word πανταχη meaning everywhere) is a maximal totally ordered subset of a partially ordered set, especially a set of equivalence classes of sequ
Domain-to-range ratio
The Domain-to-range ratio (DRR) of a logical (algorithmic) function (or software component) is the ratio of the cardinality of its set of all possible inputs (domain) to the cardinality of its set of
Kernel (set theory)
In set theory, the kernel of a function (or equivalence kernel) may be taken to be either * the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as
Definable real number
Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For exa
Vicious circle principle
The vicious circle principle is a principle that was endorsed by many predicativist mathematicians in the early 20th century to prevent contradictions. The principle states that no object or property
Diamond principle
In mathematics, and particularly in axiomatic set theory, the diamond principle ◊ is a combinatorial principle introduced by Ronald Jensen in that holds in the constructible universe (L) and that impl
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality
Hierarchy (mathematics)
In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors rese
Finitist set theory
Finitist set theory (FST) is a collection theory designed for modeling finite nested structures of individuals and a variety of transitive and antitransitive chains of relations between individuals. U
Gödel logic
In mathematical logic, a first-order Gödel logic is a member of a family of finite- or infinite-valued logics in which the sets of truth values V are closed subsets of the interval [0,1] containing bo
In mathematical set theory, a pseudo-intersection of a family of sets is an infinite set S such that each element of the family contains all but a finite number of elements of S. The pseudo-intersecti
Ordinal arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially tw
Admissible set
In set theory, a discipline within mathematics, an admissible set is a transitive set such that is a model of Kripke–Platek set theory (Barwise 1975). The smallest example of an admissible set is the
Quasi-set theory
Quasi-set theory is a formal mathematical theory for dealing with collections of objects, some of which may be indistinguishable from one another. Quasi-set theory is mainly motivated by the assumptio
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other
Boolean differential calculus
Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions. Boolean different
Ulam matrix
In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by Stanislaw Ulam in his 1930 work on measurable cardinals
List of exceptional set concepts
This is a list of exceptional set concepts. In mathematics, and in particular in mathematical analysis, it is very useful to be able to characterise subsets of a given set X as 'small', in some defini
Cantor's theorem
In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set , the set of all subsets of the power set of has a strictly greater cardinality than itself. For fin
Signed set
In mathematics, a signed set is a set of elements together with an assignment of a sign (positive or negative) to each element of the set.
Cylinder (algebra)
No description available.
Superstrong cardinal
In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j : V → M from V into a transitive inner model M with critical point κ and ⊆ M. Similarly,
Code (set theory)
In set theory, a code for a hereditarily countable set is a set such that there is an isomorphism between (ω,E) and (X,) where X is the transitive closure of {x}. If X is finite (with cardinality n),
Stationary set
In mathematics, specifically set theory and model theory, a stationary set is a set that is not too small in the sense that it intersects all club sets, and is analogous to a set of non-zero measure i
Cantor's paradise
Cantor's paradise is an expression used by David Hilbert in describing set theory and infinite cardinal numbers developed by Georg Cantor. The context of Hilbert's comment was his opposition to what h
Primitive notion
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appe
In mathematics, a corestriction of a function is a notion analogous to the notion of a restriction of a function. The duality prefix co- here denotes that while the restriction changes the domain to a
Separating set
In mathematics a set of functions S from a set D to a set C is called a separating set for D or said to separate the points of D if for any two distinct elements x and y of D, there exists a function
Support (mathematics)
In mathematics, the support of a real-valued function is the subset of the function domain containing the elements which are not mapped to zero. If the domain of is a topological space, then the suppo
Permutation model
In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. A symmetric model is similar except that it is a model
Cabal (set theory)
The Cabal was, or perhaps is, a set of set theorists in Southern California, particularly at UCLA and Caltech, but also at UC Irvine. Organization and procedures range from informal to nonexistent, so
S (set theory)
S is an axiomatic set theory set out by George Boolos in his 1989 article, "Iteration Again". S, a first-order theory, is two-sorted because its ontology includes “stages” as well as sets. Boolos desi
Cantor's first set theory article
Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his "revolutionary discov
Ideal (set theory)
In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in t
Ontological maximalism
In philosophy, ontological maximalism is a preference for largest possible universe, i.e. anything which could exist does exist.
Limit cardinal
In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from anot
Ordinal definable set
In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first-order formula. Ordinal definable sets were intr
Cumulative hierarchy
In mathematics, specifically set theory, a cumulative hierarchy is a family of sets indexed by ordinals such that * * If is a limit ordinal, then Some authors additionally require that or that . The
Game-theoretic rough sets
Game-theoretic rough sets are the use of rough sets to induce three-way classification decisions. The positive negative and boundary regions can be interpreted as regions of acceptance, rejection and
In mathematics, and particularly in axiomatic set theory, ♣S (clubsuit) is a family of combinatorial principles that are a weaker version of the corresponding ◊S; it was introduced in 1975 by Adam Ost
Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers , sometimes called the continuum. It is an infinite cardinal number and is denoted by (lowercase
Transitive reduction
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that for all pairs of vertic
Naive set theory
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics.Unlike axiomatic set theories, which are defined using formal logic, naive set theory is de
Filter (set theory)
In mathematics, a filter on a set is a family of subsets such that: 1. * and 2. * if and ,then 3. * If ,and ,then A filter on a set may be thought of as representing a "collection of large subsets"
Mathematical structure
In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the
Jensen's covering theorem
In set theory, Jensen's covering theorem states that if 0# does not exist then every uncountable set of ordinals is contained in a constructible set of the same cardinality. Informally this conclusion
Erdős–Dushnik–Miller theorem
In the mathematical theory of infinite graphs, the Erdős–Dushnik–Miller theorem is a form of Ramsey's theorem stating that every infinite graph contains either a countably infinite independent set, or
Information diagram
An information diagram is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic measures of information: entropy, joint entropy, conditional entropy and m
Controversy over Cantor's theory
In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in s
Universe (mathematics)
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a
Continuous function (set theory)
In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits (limit suprema and limit infima) of all values at previous stages. More forma
Set-builder notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the propert
Set Theory: An Introduction to Independence Proofs
Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen. It starts from basic notions, including the ZFC axioms, and quickly develops combina
Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to
Uniformization (set theory)
In set theory, a branch of mathematics, the axiom of uniformization is a weak form of the axiom of choice. It states that if is a subset of , where and are Polish spaces, then there is a subset of tha
Equaliser (mathematics)
In mathematics, an equaliser is a set of arguments where two or more functions have equal values.An equaliser is the solution set of an equation.In certain contexts, a difference kernel is the equalis
Benacerraf's identification problem
In the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument developed by Paul Benacerraf against set-theoretic Platonism and published in 1965 in an article entit
Set-theoretic limit
In mathematics, the limit of a sequence of sets (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the
Hereditarily countable set
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. This inductive definition is well-founded and can be expressed in the language of first-o
Normal function
In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if and only if it is continuous (with respect to the order topology) and strictly monotonically increasing. Th
Easton's theorem
In set theory, Easton's theorem is a result on the possible cardinal numbers of powersets. (extending a result of Robert M. Solovay) showed via forcing that the only constraints on permissible values
Dimensional operator
In mathematics, specifically set theory, a dimensional operator on a set E is a function from the subsets of E to the subsets of E.
Transitive model
In mathematical set theory, a transitive model is a model of set theory that is standard and transitive. Standard means that the membership relation is the usual one, and transitive means that the mod
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its member
Diaconescu's theorem
In mathematical logic, Diaconescu's theorem, or the Goodman–Myhill theorem, states that the full axiom of choice is sufficient to derive the law of the excluded middle, or restricted forms of it, in c
Naive Set Theory (book)
Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. Originally published by Van Nostrand in 1960, it was reprinted in the Springer-Verlag U
Willard Van Orman Quine
Willard Van Orman Quine (/kwaɪn/; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most i
Milner–Rado paradox
In set theory, a branch of mathematics, the Milner – Rado paradox, found by Eric Charles Milner and Richard Rado, states that every ordinal number less than the successor of some cardinal number can b
Goodstein's theorem
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Kirby an
Finite intersection property
In general topology, a branch of mathematics, a non-empty family A of subsets of a set is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of is no