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Slim models of Zermelo set theory

Published online by Cambridge University Press:  12 March 2014

A. R. D. Mathias
A. R. D. Mathias*
Affiliation:
Départment de Mathématiques et Informatique, Université de la Réunion, BP 7151, F97715 Saint Denis de la Réunion, Messageries Cedex 9, FranceOutre-Mer, E-mail: ardm@univ-reunion.fr, E-mail: ardm@dpmms.cam.ac.uk
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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 Φ(λ, a) such that for any sequence ⟨Aλ ∣ λ a limit ordinal⟩ where for each λ. Aλ ⊆ λ2, there is a supertransitive inner model of Zermelo containing all ordinals in which for every λAλ = {a ∣ Φ(λ, a)}.

Keywords

Zermelo set theoryfruitful classZermelo towersupertransitive model
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 487 - 496
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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