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An Example of a Complete First-Order Theory with All Models Algorithmically Trivial but Without Locally Finite Models

Article type: Research Article

Authors: Urzyczyn, Paweł

Affiliations: University of Warsaw, Institute of Mathematics

Abstract: We show an example of a first-order complete theory T, with no locally finite models and such that every program schema, total over a model of T, is strongly equivalent in that model to a loop-free schema. For this purpose we consider the notion of an algorithmically prime model, what enables us to formulate an analogue to Ryll-Nardzewski Theorem.

Keywords: program schemas, algorithmically trivial and algorithmically prime structures, eds-complete theories

DOI: 10.3233/FI-1982-53-406

Journal: Fundamenta Informaticae, vol. 5, no. 3-4, pp. 313-318, 1982

Received 20 April 1982
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Published: 1 July 1982
Price: EUR 27.50
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