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 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, iterated forcing is a method for constructing models of set theory by repeating Cohen's forcing method a transfinite number of times. Iterated...

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...

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...

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...

of a notion of forcing that preserves stationary subsets of ω1, then there is a D-generic filter. Forcing with a ccc notion of forcing preserves stationary...

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...

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...

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

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

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, 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 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...

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

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

among the "ten best" of their year by the Philosopher's Annual. Forcing (mathematics) Kenny Easwaran at Texas A&M University "The Philosopher's Annual"...

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...

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

the electric field is not conservative. For more, see Conservative force § Mathematical description. For example, in the Lorenz gauge, the electric potential...

Forcing in computability theory is a modification of Paul Cohen's original set-theoretic technique of forcing to deal with computability concerns. Conceptually...

invariants in forcing arguments. It is named for Gerald Enoch Sacks. A forcing notion is said to have the Sacks property if and only if the forcing extension...

into the RNN after each step, thus forcing the RNN to stay close to the ground-truth sequence. The term "teacher forcing" can be motivated by comparing the...

Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory...

contributions concerning forcing, large cardinals, infinite combinatorics and their applications to other areas of mathematics. Bagaria was born in 1958...