Model companion of ordered theories with an automorphism
Authors:
Michael C. Laskowski and Koushik Pal
Journal:
Trans. Amer. Math. Soc. 367 (2015), 6877-6902
MSC (2010):
Primary 03C10, 03C64; Secondary 20K30, 20A05
DOI:
https://doi.org/10.1090/S0002-9947-2015-06496-4
Published electronically:
February 12, 2015
MathSciNet review:
3378817
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal {L}$, then in the expanded language $\mathcal {L}_\sigma := \mathcal {L}\cup \{\sigma \}$ with a new unary function symbol $\sigma$, the bigger theory $T_\sigma := T\cup \{“\sigma \mbox { is an } \mathcal {L}\mbox {-automorphism''}\}$ does not have a model companion. We show in this paper that if, however, we restrict the automorphism and consider the theory $T_\sigma$ as the base theory $T$ together with a “restricted” class of automorphisms, then $T_\sigma$ can have a model companion in $\mathcal {L}_\sigma$. We show this in the context of linear orders and ordered abelian groups.
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Additional Information
Michael C. Laskowski
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
mcl@math.umd.edu
Koushik Pal
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
koushik@math.umd.edu
Received by editor(s):
May 31, 2013
Published electronically:
February 12, 2015
Additional Notes:
The authors were partially supported by the first author’s NSF grant DMS-0901336.
Article copyright:
© Copyright 2015
American Mathematical Society
