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- Forcing (mathematics)

Collapsing algebra

In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduce

Generic filter

In the mathematical field of set theory, a generic filter is a kind of object used in the theory of forcing, a technique used for many purposes, but especially to establish the independence of certain

Complete Boolean algebra

In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set t

Cohen algebra

In mathematical set theory, a Cohen algebra, named after Paul Cohen, is a type of Boolean algebra used in the theory of forcing. A Cohen algebra is a Boolean algebra whose completion is isomorphic to

Random algebra

In set theory, the random algebra or random real algebra is the Boolean algebra of Borel sets of the unit interval modulo the ideal of measure zero sets. It is used in random forcing to add random rea

Martin's maximum

In set theory, a branch of mathematical logic, Martin's maximum, introduced by and named after Donald Martin, is a generalization of the proper forcing axiom, itself a generalization of Martin's axiom

Iterated forcing

In mathematics, iterated forcing is a method for constructing models of set theory by repeating Cohen's forcing method a transfinite number of times. Iterated forcing was introduced by Solovay and Ten

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

Forcing (mathematics)

In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results. It was first used by Paul Cohen in 1963, to prove the independence of the axiom o

Laver property

In mathematical set theory, the Laver property holds between two models if they are not "too dissimilar", in the following sense. For and transitive models of set theory, is said to have the Laver pro

Proper forcing axiom

In the mathematical field of set theory, the proper forcing axiom (PFA) is a significant strengthening of Martin's axiom, where forcings with the countable chain condition (ccc) are replaced by proper

Boolean-valued model

In mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not li

Amoeba order

In mathematics, the amoeba order is the partial order of open subsets of 2ω of measure less than 1/2, ordered by reverse inclusion. Amoeba forcing is forcing with the amoeba order; it adds a measure 1

Sacks property

In mathematical set theory, the Sacks property holds between two models of Zermelo–Fraenkel set theory if they are not "too dissimilar" in the following sense. For and transitive models of set theory,

List of forcing notions

In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M. The poset P used will determine what statements hold in the ne

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

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

Ramified forcing

In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by to prove the independence of the continuum hypothesis from Zermelo–Fraenkel set theory. Ram

Countable chain condition

In order theory, a partially ordered set X is said to satisfy the countable chain condition, or to be ccc, if every strong antichain in X is countable.

Rasiowa–Sikorski lemma

In axiomatic set theory, the Rasiowa–Sikorski lemma (named after Helena Rasiowa and Roman Sikorski) is one of the most fundamental facts used in the technique of forcing. In the area of forcing, a sub

Cantor algebra

In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all c

Nice name

In set theory, a nice name is used in forcing to impose an upper bound on the number of subsets in the generic model. It is used in the context of forcing to prove independence results in set theory s

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