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

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

2008-07-30

arxiv.org/abs/0807.4938v1

Mathematics

Logic

12 pages, no figures

Scientific paper

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.

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