Theories with EF-Equivalent Non-Isomorphic Models
逻辑
2017-08-08 v3
摘要
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).
引用
@article{arxiv.math/0703477,
title = {Theories with EF-Equivalent Non-Isomorphic Models},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0703477},
year = {2017}
}