arXiv:2001.09243 Abstract | arXiv Analytics

arXiv:2001.09243 [math.LO]Abstract References Reviews Resources

A Barwise-Schlipf Theorem for Set Theory

Published 2020-01-25Version 1

We characterize nonstandard models of ZF (Zermelo-Fraenkel) set theory (of arbitrary cardinality) that can be expanded to Goedel-Bernays class theory plus $\Delta^1_1$-Comprehension. We also characterize countable nonstandard models of ZFC (ZF with the axiom of choice) that can be expanded to Goedel-Bernays class theory plus $\Sigma^1_1$-Choice.

Comments: 14 pages

Categories: math.LO

Subjects: 03C62, 03E30

Keywords: set theory, barwise-schlipf theorem, goedel-bernays class theory plus, arbitrary cardinality, characterize nonstandard models

Related articles: Most relevant | Search more

arXiv:1911.05117 [math.LO] (Published 2019-11-12)

The Barwise-Schlipf Theorem

Ali Enayat, James H. Schmerl

arXiv:1707.04660 [math.LO] (Published 2017-07-14)

The classification of countable models of set theory

John Clemens, Samuel Coskey, Samuel Dworetzky

arXiv:0709.2436 [math.LO] (Published 2007-09-15)