Complete theories with finitely many countable models. II |
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Authors: | S V Sudoplatov |
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Institution: | (1) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia |
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Abstract: | Previously, we obtained a syntactic characterization for the class of complete theories with finitely many pairwise non-isomorphic
countable models 1]. The most essential part of that characterization extends to Ehrenfeucht theories (i.e., those having
finitely many (but more than 1) pairwise non-isomorphic countable models). As the basic parameters defining a finite number
of countable models, Rudin-Keisler quasiorders are treated as well as distribution functions defining the number of limit
models for equivalence classes w.r.t. these quasiorders. Here, we argue to state that all possible parameters given in the
characterization theorem in 1] are realizable. Also, we describe Rudin-Keisler quasiorders in arbitrary small theories. The
construction of models of Ehrenfeucht theories with which we come up in the paper is based on using powerful digraphs which,
along with powerful types in Ehrenfeucht theories, always locally exist in saturated models of these theories.
Supported by RFBR grant Nos. 02-01-00258 and 05-01-00411.
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Translated from Algebra i Logika, Vol. 45, No. 3, pp. 314–353, May–June, 2006. |
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Keywords: | complete theory Ehrenfeucht theory number of countable models Rudin-Keisler quasiorder |
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