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September 2004 Leibnizian models of set theory
Ali Enayat
J. Symbolic Logic 69(3): 775-789 (September 2004). DOI: 10.2178/jsl/1096901766

Abstract

A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the Leibniz-Mycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF, T has a Leibnizian model if and only if T proves LM. Here we prove: Theorem 1 Every complete theory T extending ZF+LM has 20 nonisomorphic countable Leibnizian models. Theorem 2 If κ is a prescribed definable infinite cardinal of a complete theory T extending ZF+V=OD, then there are 21 nonisomorphic Leibnizian models 𝔐 of T of power ℵ1 such that (κ+)𝔐 is ℵ1-like. Theorem 3 Every complete theory T extending ZF+V=OD has 21 nonisomorphic ℵ1-like Leibnizian models.

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Ali Enayat. "Leibnizian models of set theory." J. Symbolic Logic 69 (3) 775 - 789, September 2004. https://doi.org/10.2178/jsl/1096901766

Information

Published: September 2004
First available in Project Euclid: 4 October 2004

zbMATH: 1070.03023
MathSciNet: MR2078921
Digital Object Identifier: 10.2178/jsl/1096901766

Subjects:
Primary: 03C50 , 03C62
Secondary: 03H99

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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