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Words near each other
・ Nice Guy Eddie
・ Nice Guy Johnny
・ Nice Guys
・ Nice Guys (album)
・ Nice Guys (song)
・ Nice Guys Finish First
・ Nice Guys Finish Last
・ Nice Guys Sleep Alone
・ Nice Ideas
・ Nice Is Different Than Good
・ Nice Jazz Festival
・ Nice Lawn Tennis Club
・ Nice metropolitan area
・ Nice model
・ Nice na Kokoroiki
Nice name
・ Nice Observatory
・ Nice Package
・ Nice People
・ Nice People (disambiguation)
・ Nice People (play)
・ Nice People (TV France)
・ Nice Place to Visit
・ Nice Price! (album)
・ Nice Ride Minnesota
・ Nice She Ain't
・ Nice Shoes
・ Nice Shootin' Cowboy
・ Nice subgroup
・ NICE Systems


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Nice name : ウィキペディア英語版
Nice name
In set theory, a nice 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 results in set theory such as Easton's theorem.
==Formal definition==
Let M \models ZFC be transitive, (\mathbb, <) a forcing notion in M, and suppose G \subseteq \mathbb is generic over M. Then for any \mathbb-name in M, \tau,
\eta is a nice name for a subset of \tau if \eta is a \mathbb-name satisfying the following properties:
(1) \textrm(\eta) \subseteq \textrm(\tau)
(2) For all \mathbb-names \sigma \in M, \ forms an antichain.
(3) (Natural addition): If \langle\sigma, p\rangle \in \eta, then there exists q \geq p in \mathbb such that \langle\sigma, q\rangle \in \tau.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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