Constructing many atomic models in ℵ1

John T. Baldwin; Michael C. Laskowski; Saharon Shelah

doi:10.1017/jsl.2015.81

Constructing many atomic models in ℵ₁

John T. Baldwin, Michael C. Laskowski, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We introduce the notion of pseudoalgebraicity to study atomic models of first order theories (equivalently models of a complete sentence of L_ω₁,_ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudominimal types are not dense, then there are 2^ℵ¹ pairwise nonisomorphic atomic models of T, each of size ℵ₁.

Original language	English
Pages (from-to)	1142-1162
Number of pages	21
Journal	Journal of Symbolic Logic
Volume	81
Issue number	3
DOIs	https://doi.org/10.1017/jsl.2015.81
State	Published - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Association for Symbolic Logic.

Keywords

Atomic models
Forcing
Infinitary logic
Pseudo-minimality

Access to Document

10.1017/jsl.2015.81

Cite this

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