# Category: Independence results

Kanamori–McAloon theorem
In mathematical logic, the Kanamori–McAloon theorem, due to , gives an example of an incompleteness in Peano arithmetic, similar to that of the Paris–Harrington theorem. They showed that a certain fin
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
Wetzel's problem
In mathematics, Wetzel's problem concerns bounds on the cardinality of a set of analytic functions that, for each of their arguments, take on few distinct values. It is named after John Wetzel, a math
In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Is every abelian group A with Ext1(A, Z) = 0 a free abelian group? Saharon Shelah proved that Whitehead'
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
Moore space (topology)
In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold: * Any t
Paris–Harrington theorem
In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano ar
Suslin tree
In mathematics, a Suslin tree is a tree of height ω1 such thatevery branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn
Suslin's problem
In mathematics, Suslin's problem is a question about totally ordered sets posed by Mikhail Yakovlevich Suslin and published posthumously.It has been shown to be independent of the standard axiomatic s
Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the in
Jech–Kunen tree
A Jech–Kunen tree is a set-theoretic tree with properties that are incompatible with the generalized continuum hypothesis. It is named after Thomas Jech and Kenneth Kunen, both of whom studied the pos
Suslin algebra
In mathematics, a Suslin algebra is a Boolean algebra that is complete, atomless, countably distributive, and satisfies the countable chain condition. They are named after Mikhail Yakovlevich Suslin.
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
Kurepa tree
In set theory, a Kurepa tree is a tree (T, <) of height ω1, each of whose levels is at most countable, and has at least ℵ2 many branches. This concept was introduced by Kurepa. The existence of a Kure
Aronszajn tree
In set theory, an Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn tree. More generally, for a card
Naimark's problem
Naimark's problem is a question in functional analysis asked by Naimark. It asks whether every C*-algebra that has only one irreducible -representation up to unitary equivalence is isomorphic to the -
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
Strong measure zero set
In mathematical analysis, a strong measure zero set is a subset A of the real line with the following property: for every sequence (εn) of positive reals there exists a sequence (In) of intervals such
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