Gavryushkin, Alexander On constructive models of theories with linear Rudin-Keisler ordering. (English) Zbl 1260.03069 J. Log. Comput. 22, No. 4, 793-805 (2012). 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 Keywords:Ehrenfeucht theory; Rudin-Keisler order; decidable theory; decidable model; computable model PDFBibTeX XMLCite \textit{A. Gavryushkin}, J. Log. Comput. 22, No. 4, 793--805 (2012; Zbl 1260.03069) Full Text: DOI