魔杖/集合理论:实现康威的数学家解放运动,并应用于具有普遍集合的教会集合论

TIM BUTTON
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引用次数: 0

摘要

考虑一下关于集合的迭代概念的通常故事的变体。像往常一样,在每个阶段,你都能找到之前找到的所有(平淡无奇的)物体集合。通过改变魔杖的数量和行为,我们可以用许多不同的方法来充实这个想法。本文的主要定理是,充实这一思想的任何松散的构造性方法都是类似 ZF 的理论的同义词。这个定理有着丰富的应用;它实现了约翰-康威(John Conway,1976 年)的数学家解放运动;它还与阿朗佐-丘奇(Alonzo Church,1974 年)的一个可爱的想法相联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
WAND/SET THEORIES: A REALIZATION OF CONWAY’S MATHEMATICIANS’ LIBERATION MOVEMENT, WITH AN APPLICATION TO CHURCH’S SET THEORY WITH A UNIVERSAL SET

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands).

By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory.

This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974).

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