Leibnizian models of set theory

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

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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1096901766
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,062
Through your library

References found in this work BETA

Add more references

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 - forthcoming - Mathematical Logic Quarterly.

Add more citations

Similar books and articles


Added to PP index

Total views
32 ( #229,677 of 2,320,192 )

Recent downloads (6 months)
6 ( #232,023 of 2,320,192 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature