The Number of Fragments of the Perfect Class of the Jonsson Spectrum

Aibat R. Yeshkeyev, O.I. Ulbrikht, M.T. Omarova

2022

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DOI 10.1134/s199508022215029x
Data confidence 70 medium
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Abstract

Abstract In this article, we consider the notion of the Jonsson spectrum of some subclass of existentially closed models of a fixed Jonsson theory. For an arbitrary model of an arbitrary signature, the class of existentially closed models in that signature is considered, in which this arbitrary model is isomorphically embedded. The model-theoretical properties of the Kaiser Hull of this class are studied. In the language of central types of permissible enrichments, the properties of the considered fragments for special definable subsets of the semantic model of a fixed Jonsson theory are studied. The main result of this work is an estimate of the number of such fragments.