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Constructing many atomic models in ℵ1

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journal contribution
posted on 19.12.2016, 00:00 authored by JT Baldwin, MC Laskowski, S Shelah
We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are 2 ℵ1 pairwise non-isomorphic atomic models of T, each of size ℵ1.

Funding

Research partially supported by Simons travel grant G5402 Partially supported by NSF grant DMS-1308546.This research was partially supported by NSF grant DMS 1101597. The third author was partially supported by the European Research Council grant 338821.

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Publisher Statement

This is a non-final version of an article published in final form in: Baldwin, J. T., Laskowski, M. C. and Shelah, S. CONSTRUCTING MANY ATOMIC MODELS IN N-1. Journal of Symbolic Logic. 2016. 81(3): 1142-1162. DOI: 10.1017/jsl.2015.81.

Publisher

Association for Symbolic Logic

issn

0022-4812

Issue date

01/09/2016

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