In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results. Intuitively, forcing can be thought...

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...

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...

Look up forcing in Wiktionary, the free dictionary. Forcing may refer to: Forcing (mathematics), a technique for obtaining independence proofs for set...

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...

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states:...

the statement of Martin's axiom. In the theory of forcing, ccc partial orders are used because forcing with any generic set over such an order preserves...

Unsolved problem in mathematics: For any sunflower size, does every set of uniformly sized sets which is of cardinality greater than some exponential...

In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are...

of forcing while searching for a model of ZFC in which the continuum hypothesis fails, or a model of ZF in which the axiom of choice fails. Forcing adjoins...

Criticism of non-standard analysis Standard part function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic...

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...

In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by Cohen (1963) to prove the independence of...

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant...

of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics. The mathematical field...

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...

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

others found deep new results in mathematical logic and axiomatic set theory using offshoots of Boolean algebra, namely forcing and Boolean-valued models. A...

one of the most fundamental facts used in the technique of forcing. In the area of forcing, a subset E of a poset (P, ≤) is called dense in P if for any...

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...

syntactic forcing A forcing relation p ⊩ ϕ {\displaystyle p\Vdash \phi } is defined between elements p of the poset and formulas φ of the forcing language...

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

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...

Axiom of projective determinacy Axiom of real determinacy Empty set Forcing (mathematics) Fuzzy set Hereditary set Internal set theory Intersection (set theory)...

Effective enumeration Element (mathematics) Empty function Empty set Enumeration Extensionality Finite set Forcing (mathematics) Function (set theory) Function...

in the domain of G. The proof of Easton's theorem uses forcing with a proper class of forcing conditions over a model satisfying the generalized continuum...

unit interval modulo the ideal of measure zero sets. It is used in random forcing to add random reals to a model of set theory. The random algebra was studied...

Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major...

In mathematics and physics, vector is a term that refers to quantities that cannot be expressed by a single number (a scalar), or to elements of some...