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Forcing A Passage Of The Hudson
Forcing may refer to: Mathematics and science *Forcing (mathematics), a technique for obtaining independence proofs for set theory * Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with the effective concerns in recursion theory *Forcing, driving a harmonic oscillator at a particular frequency *Cloud forcing, the difference between the radiation budget components for average cloud conditions and cloud-free conditions * Forcing bulbs, the inducement of plants to flower earlier than their natural season *Radiative forcing, the difference between the incoming radiation energy and the outgoing radiation energy in a given climate system Arts, entertainment, and media *Forcing (magic), a technique by which a magician forces one outcome from a card draw * Forcing, several distinct concepts within the game of contract bridge: ** Forcing bid ** Forcing defense ** Forcing notrump ** Forcing pass ** Forcing take-out, an obsolete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 notions 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. Intuition Intuitively, forcing consists of expanding the set theoretical universe V to a larger universe V^ . In this bigger universe, for example, one might have many new real numbers, identified with subsets of the set \mathbb of natural numbers, that were not there in the old ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |