### 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.

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This work was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant AP09260237).

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(Submitted byM. M. Arslanov)

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Yeshkeyev, A.R., Ulbrikht, O.I. & Omarova, M.T. The Number of Fragments of the Perfect Class of the Jonsson Spectrum.
*Lobachevskii J Math* **43**, 3658–3673 (2022). https://doi.org/10.1134/S199508022215029X

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DOI: https://doi.org/10.1134/S199508022215029X