arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0807.4938math.LO
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ZFK:=带补语的ZFC,或:黑格尔与合成集合论

ZFK := ZFC with a Complement, or: Hegel and the Synto-Set-Theory

Werner DePauli-Schimanovich

摘要:

如果要在ZF中添加一个补公理,最轻微的修改是什么?在我的博士论文中,1971年的论文是ZF“:Zermelo-Fraenkel with replacement for only well-founded domains and an omega-axiom。1974年,阿朗佐·丘奇(Alonzo Church)发表了一个类似的系统,1976年,乌尔斯·奥斯瓦尔德(Urs Oswald)也发表了类似的系统。在1976年的博士学位。thesis,E.米切尔还设计了一个非常类似于ZF的系统。在这篇文章中,我们认为ZF“是ZF在所有这些系统中的最小修改,它的后继者ZFK是具有全集的最简单的集合论。

英文摘要:

What is the slightest modification of ZF to add a complement-axiom? The answer in my Ph.D. thesis 1971 was ZF'': Zermelo-Fraenkel with replacement for only well-founded domains and an omega-axiom. In 1974, Alonzo Church published a similar system, as did Urs Oswald in 1976. In his 1976 Ph.D. thesis, E. Mitchell also designed, a system very similar to ZF''. In this article we argue that ZF'' is the slightest modification of ZF among all these systems and that its successor ZFK is the simplest set theory with a universal set at all.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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