## Journal of Symbolic Logic

### Slim Models of Zermelo Set Theory

A. R. D. Mathias

#### 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

https://projecteuclid.org/euclid.jsl/1183746455

Mathematical Reviews number (MathSciNet)
MR1833460

Zentralblatt MATH identifier
0989.03049

JSTOR