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Preprint Number 588
588. Michael C. Laskowski and Koushik Pal Model companion of ordered theories with an automorphism E-mail: Submission date: 31 May 2013. Abstract: 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 Keywords and phrases: |
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