Abstract
In the present article, we obtain a new criterion for amodel of a universally axiomatizable theory to be existentially closed. The notion of a maximal existential type is used in the proof and for investigating properties of countable infinite existentially closed structures. The notions of a prime and a homogeneous model, which are classical for the general model theory, are introduced for such structures. We study universal theories with the joint embedding property admitting a single countable infinite existentially closed model. We also construct, for every natural n, an example of a complete inductive theory with a countable infinite family of countable infinite models such that n of them are existentially closed and exactly two are homogeneous.
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Original Russian Text © A.T. Nurtazin, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 1, pp. 48–97.
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Nurtazin, A.T. Countable infinite existentially closed models of universally axiomatizable theories. Sib. Adv. Math. 26, 99–125 (2016). https://doi.org/10.3103/S1055134416020036
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DOI: https://doi.org/10.3103/S1055134416020036