Journal of Symbolic Logic 66 (2):487-496 (2001)

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 $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A λ = {α ∣Φ(λ, a)}
Keywords Zermelo Set Theory   Fruitful Class   Zermelo Tower   Supertransitive Model
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DOI 10.2307/2695026
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References found in this work BETA

Happy Families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Elements of Set Theory.Herbert B. Enderton - 1981 - Journal of Symbolic Logic 46 (1):164-165.
Mengeninduktion und Fundierungsaxiom.Ronald Björn Jensen & Max E. Schröder - 1969 - Archive for Mathematical Logic 12 (3-4):119-133.

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Citations of this work BETA

The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
Mathematical Existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.
Zermelo and Set Theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.

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