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单词 Generic extension
释义

Generic extension

中文百科

力迫 Forcing (mathematics)

(重定向自Generic extension)

在数学学科集合论中,力迫是 保罗·寇恩(Paul J. Cohen)发明的一种技术,用来证明与策梅洛-弗兰克尔公理有关的一致性和独立性结果。它在1962年首次被用来证明连续统假设和选择公理对策梅洛-弗兰克尔集合论的独立性。实际上在寇恩正式引入力迫法前,它已经被广泛地应用于递归论中。寇恩的力迫法最初是创建在分歧分层(ramified hierarchy)上,难于理解。1960年代通过索罗维(Solovay)与斯科特(Scott)等人的努力力迫法被相当程度的重做和简化。

力迫法大致是一种扩张模型的方法。给定一个模型M以及模型内一个偏序(P,\leq),通过构造通集(generic)G\subseteq P来实现模型的扩张。因为通集不在M内,所以这是一个真正的扩张。记为M[G]。它有以下性质:

英语百科

Forcing (mathematics) 力迫

(重定向自Generic extension)

In the mathematical discipline of set theory, forcing is a technique discovered by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory. Forcing was 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.

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更新时间:2025/6/22 18:01:09