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Mathematics > Logic

arXiv:math/0703477 (math)
[Submitted on 16 Mar 2007 (v1), last revised 7 Aug 2017 (this version, v3)]

Title:Theories with EF-Equivalent Non-Isomorphic Models

Authors:Saharon Shelah
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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 lambda,M_1,M_2 such that M_1,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 we get a strong dichotomy, so in the non-structure side we have stronger, better examples, and in the structure side we have a parallel of [Sh:c,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).
Subjects: Logic (math.LO)
Report number: Shelah [Sh:897]
Cite as: arXiv:math/0703477 [math.LO]
  (or arXiv:math/0703477v3 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.math/0703477

Submission history

From: shlhetal [view email] [via Saharon Shelah as proxy]
[v1] Fri, 16 Mar 2007 01:10:42 UTC (37 KB)
[v2] Wed, 15 Aug 2007 02:31:31 UTC (44 KB)
[v3] Mon, 7 Aug 2017 12:46:29 UTC (36 KB)
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