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Fundamentalnaya i Prikladnaya Matematika, 2009, Volume 15, Issue 7, Pages 179–203
(Mi fpm1277)
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This article is cited in 14 scientific papers (total in 14 papers)
Hypergraphs of prime models and distributions of countable models of small theories
S. V. Sudoplatov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
Hypergraphs of prime models over realizations of types in small theories are defined. On the basis of graph structures of models of small theories, hierarchies of sets in these hypergraphs, revealing structural connections in countable models of small theories, are established. The key role of graph-theoretic objects in constructions of Ehrenfeucht theories is proved. Using hypergraph constructions, a classification of complete first-order theories with finite Rudin–Keisler preorders is generalized to the class of all small theories.
Citation:
S. V. Sudoplatov, “Hypergraphs of prime models and distributions of countable models of small theories”, Fundam. Prikl. Mat., 15:7 (2009), 179–203; J. Math. Sci., 169:5 (2010), 680–695
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https://www.mathnet.ru/eng/fpm1277 https://www.mathnet.ru/eng/fpm/v15/i7/p179
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Abstract page: | 346 | Full-text PDF : | 135 | References: | 47 | First page: | 1 |
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