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On constructive models of theories with linear Rudin-Keisler ordering. (English) Zbl 1260.03069

Summary: It is known that the class of Ehrenfeucht theories admits a syntactical characterization and that a finite (Rudin-Keisler) pre-ordering and a function mapping this pre-ordering to naturals play the role of parameters in this characterization. In the article, we construct for any finite linear ordering \(L\), a hereditary decidable Ehrenfeucht theory \(T\) possessing \(L\) as its Rudin-Keisler pre-ordering. Also, we discuss decidable and computable models of such theories.

MSC:

03C57 Computable structure theory, computable model theory
03B25 Decidability of theories and sets of sentences
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