Journal of Symbolic Logic 69 (3):775-789 (2004)

Authors
Ali Enayat
University of Gothenburg
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 A. Every complete theory T extending ZF + LM has $2^{\aleph_{0}}$ nonisomorphic countable Leibnizian models. THEOREM B. If $\kappa$ is aprescribed definable infinite cardinal of a complete theory T extending ZF + V = OD. then there are $2^{\aleph_{1}}$ nonisomorphic Leibnizian models $\mathfrak{M}$ of T of power $\aleph_{1}$ such that $(\kappa^{+})^\mathfrak{M}$ is $\aleph_{1}-like$ . THEOREM C. Every complete theory T extending ZF + V = OD has $2^{\aleph_{1}}$ nonisomorphic \aleph_{1}-like$ Leibnizian models
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DOI 10.2178/jsl/1096901766
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Set Theory and the Continuum Hypothesis.Kenneth Kunen - 1966 - Journal of Symbolic Logic 35 (4):591-592.
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Truth, Disjunction, and Induction.Ali Enayat & Fedor Pakhomov - 2019 - Archive for Mathematical Logic 58 (5-6):753-766.

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Citations of this work BETA

Models of Set Theory with Definable Ordinals.Ali Enayat - 2004 - Archive for Mathematical Logic 44 (3):363-385.
Rigid Models of Presburger Arithmetic.Emil Jeřábek - 2019 - Mathematical Logic Quarterly 65 (1):108-115.
Ehrenfeucht’s Lemma in Set Theory.Gunter Fuchs, Victoria Gitman & Joel David Hamkins - 2018 - Notre Dame Journal of Formal Logic 59 (3):355-370.

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