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Preprint Number 588

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588. Michael C. Laskowski and Koushik Pal
Model companion of ordered theories with an automorphism

Submission date: 31 May 2013.


Kikyo and Shelah showed that if T is a theory with the Strict Order Property in some first-order language L, then in the expanded language L_\sigma := L\cup {\sigma} with a new unary function symbol \sigma, the bigger theory T_\sigma := T\cup {“\sigma is an L-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 &#!47;restricted” class of automorphisms, then T_\sigma can have a model companion in L_\sigma. We show this in the context of linear orders and ordered abelian groups.

Mathematics Subject Classification: Primary 03C10, 03C64, Secondary 20K30, 20A05

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Full text arXiv 1305.7501: pdf, ps.

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