Part of USAF

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Possible Answers: FORCE.

Last seen on: Newsday.com Crossword – Dec 3 2017

Random information on the term “FORCE”:

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 of choice and the continuum hypothesis from Zermelo–Fraenkel set theory.

Forcing 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 recursion theory. Descriptive set theory uses the notion of forcing from both recursion 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.

Intuitively, forcing consists of expanding the set theoretical universe V {\displaystyle V} to a larger universe V ∗ {\displaystyle V^{*}} . In this bigger universe, for example, one might have many new subsets of ω {\displaystyle \omega } = { 0 , 1 , 2 , … } {\displaystyle =\{0,1,2,\ldots \}} that were not there in the old universe, and thereby violate the continuum hypothesis.

FORCE on Wikipedia