F

Forcing (mathematics)

In set theory, a technique for enlarging models of axioms of set theory (e.g. ZFC) by adjoining new elements, often used for proving consistency and independence results

In set theory, forcing is a technique for proving consistency and independence results. Intuitively, forcing can be thought of as a technique to expand the set theoretical universe V {\displaystyle V} to a larger universe V [ G ] {\displaystyle V[G]} by introducing a new "generic" object G {\displaystyle G} .

Nº Q1003136 ★

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Forcing (mathematics)

In set theory, a technique for enlarging models of axioms of set theory (e.g. ZFC) by adjoining new elements, often used for proving consistency and independence results

In set theory, forcing is a technique for proving consistency and independence results. Intuitively, forcing can be thought of as a technique to expand the set theoretical universe V {\displaystyle V} to a larger universe V [ G ] {\displaystyle V[G]} by introducing a new "generic" object G {\displaystyle G} .

From Wikipedia

In set theory, forcing is a technique for proving consistency and independence results. Intuitively, forcing can be thought of as a technique to expand the set theoretical universe V {\displaystyle V} to a larger universe V [ G ] {\displaystyle V[G]} by introducing a new "generic" object G {\displaystyle G} . Forcing was first used by Paul Cohen in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory. It has been considerably reworked and simplified in the following years, and has since served as a powerful technique, both in set theory and in areas of mathematical logic such as computability theory. Descriptive set theory uses the notions of forcing from both computability theory and set theory. Forcing has also been used in model theory, but it is common in model theory to define genericity directly without mention of forcing.

Text: Wikipédia, CC BY-SA 4.0. ·

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