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2008 Theories with Ehrenfeucht-Fraïssé equivalent non-isomorphic models
Saharon Shelah
Author Affiliations +
Tbilisi Math. J. 1: 133-164 (2008). DOI: 10.32513/tbilisi/1528768827

Abstract

Our “long term and large scale” aim is to characterize the first order theories $T$ (at least the countable ones) such that for every ordinal $\alpha$ there are $\lambda$, $M_1$, $M_2$ such that $M_1$ and $M_2$ are non-isomorphic models of $T$ of cardinality $\lambda$ which are EF$^+_{\alpha,\lambda}$-equivalent. We expect that as in the main gap [11, XII], we get a strong dichotomy, i.e., on the non-structure side we have stronger, better examples, and on the structure side we have an analogue of [11, XIII]. We presently prove the consistency of the non-structure side for $T$ which is $\aleph_0$-independent (= not strongly dependent), even for PC$(T_1,T)$.

Funding Statement

The author would like to thank the Israel Science Foundation for partial support of this research (Grant Number 242/03), Alice Leonhardt for the beautiful typing and the three anonymous referees for many helpful remarks. Particular thanks are due to one referee who pointed out that an earlier version of this paper did not contain anything new beyond [2]; Definition 2.5 now fixes this problem. This paper is publication number 897 of the list of the author's publications.

Citation

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Saharon Shelah. "Theories with Ehrenfeucht-Fraïssé equivalent non-isomorphic models." Tbilisi Math. J. 1 133 - 164, 2008. https://doi.org/10.32513/tbilisi/1528768827

Information

Received: 16 March 2008; Revised: 15 August 2008; Accepted: 25 October 2008; Published: 2008
First available in Project Euclid: 12 June 2018

zbMATH: 1158.03315
MathSciNet: MR2563810
Digital Object Identifier: 10.32513/tbilisi/1528768827

Subjects:
Primary: 03C55
Secondary: 03C68, 03E40

Rights: Copyright © 2008 Tbilisi Centre for Mathematical Sciences

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