Journal of Symbolic Logic

Slim Models of Zermelo Set Theory

A. R. D. Mathias

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Abstract

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi(\lambda, a)$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha \mid\Phi(\lambda, a)\}$.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 2 (2001), 487-496.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746455

Mathematical Reviews number (MathSciNet)
MR1833460

Zentralblatt MATH identifier
0989.03049

JSTOR
links.jstor.org

Subjects
Primary: 03C30: Other model constructions
Secondary: 03E30: Axiomatics of classical set theory and its fragments 03E45: Inner models, including constructibility, ordinal definability, and core models

Keywords
Zermelo Set Theory Fruitful Class Zermelo Tower Supertransitive Model

Citation

Mathias, A. R. D. Slim Models of Zermelo Set Theory. J. Symbolic Logic 66 (2001), no. 2, 487--496. https://projecteuclid.org/euclid.jsl/1183746455


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