Internal hybridization of Kaiser hulls and Morley-type criteria in KT-normal Jonsson theories
DOI:
https://doi.org/10.31489/2026m3/130-141Keywords:
Jonsson theory, Kaiser class, Kaiser hull, internal hybridization, hybrid model, hybrid spectrum, categoricity criterion, model perfection, model completeness, prime extensionAbstract
This article examines the internal hybridization of Kaiser hulls in Jonsson theory and the transfer of classical spectral properties to hybrid settings. The relevance of this study is determined by the need to distinguish internal hybrid constructions generated within a fixed Kaiser class from external hybrids of unrelated theories. The characteristic features of such internal constructions are analyzed within the framework of a fixed Kaiser-normal Jonsson theory. The necessity of stability conditions that preserve the Kaiser hull under admissible hybrid unification is identified and justified. Based on the conducted research, hybridization is considered as an internal operation on semantic fragments of a Jonsson theory. A technical criterion ensuring the preservation of the ambient Kaiser class of the semantic model under internal hybrid is formulated. We prove that, under Kaiser-normality, the semantic model of a hybrid remains within the original Kaiser class. It is shown that this fact makes it possible to transfer Morley-type categoricity criteria, Saracino-type perfection arguments, and Lindstro¨m-type model-completeness principles to Jonsson hybrid spectra. As a result, hybrid analogues of results on prime extensions, model perfection, and model completeness are obtained.
References
Barwise, J. (Ed.). (1977). Handbook of mathematical logic. Studies in Logic and the Foundations of Mathematics. (Vol. 90). Amsterdam: North-Holland.
Yeshkeyev, A.R. (2024). Teorii i ikh modeli [Theories and their models]: monograph. (Vols. 1–2). Karaganda: Izdatelstvo KarU [in Russian].
Yeshkeyev, A.R., Tungushbayeva, I.O., & Ulbrikht, O. (2024). On some types of algebras of a Jonsson spectrum. Siberian Electronic Mathematical Reports, 21(2), 866–881. https://doi.org/10.33048/semi.2024.21.057
Yeshkeyev, A.R., Ulbrikht, O.I., & Mussina, N.M. (2023). Similarities of hybrids from Jonsson spectrum and S-acts. Lobachevskii Journal of Mathematics, 44(12), 5502–5518. https://doi.org/10.1134/S1995080223120399
Kassymetova, M.T., Tungushbayeva, I.O., & Yarullina, A.R. (2025). Syntactic similarity of hybrids of classes of normal Jonsson theories. Actual Problems of Analysis, Differential Equations and Algebra (EMJ-2025): International Conference dedicated to the 15th anniversary of the Eurasian Mathematical Journal, 163–164.
Yeshkeyev, A.R., Omarova, M.T., & Ulbrikht, O.I. (2025). Normality and similarity in the Jonsson spectrum. Actual Problems of Analysis, Differential Equations and Algebra (EMJ-2025): International Conference dedicated to the 15th anniversary of the Eurasian Mathematical Journal, 179–180.
Yeshkeyev, A., Tungushbayeva, I., & Kassymetova, M. (2025). On the Kaiser class of a Jonsson theory. Symmetry, 17(6), 870. https://doi.org/10.3390/sym17060870
Yeshkeyev, A.R., Tungushbayeva, I.O., & Kassymetova, M.T. (2025). The properties of clnormal Jonsson theories and their Kaiser classes. Traditional International April Mathematical Conference in honor of the Science Day of the Republic of Kazakhstan, the 80th anniversary of the Sector of Mathematics and Mechanics of the Kazakh Branch of the USSR Academy of Sciences and the 60th anniversary of the Institute of Mathematics and Mathematical Modeling, 293.
Yeshkeyev, A.R., Yarullina, A.R., & Kassymetova, M.T. (2025). On Kaiser class of unars in expanded signature. Traditional International April Mathematical Conference in honor of the Science Day of the Republic of Kazakhstan, the 80th anniversary of the Sector of Mathematics and Mechanics of the Kazakh Branch of the USSR Academy of Sciences and the 60th anniversary of the Institute of Mathematics and Mathematical Modeling, 295–297.
Zhumabekova, G.E. (2023). Model-theoretic properties of semantic pairs and e.f.c.p. in Jonsson spectrum. Bulletin of the Karaganda University. Mathematics Series, 4(112), 185–193. https://doi.org/10.31489/2023M4/185-193
Kassymetova, M.T., & Zhumabekova, G.E. (2024). Model-theoretic properties of J-non-multidimensional theories. Bulletin of the Karaganda University. Mathematics Series, 4(116), 119–126. https://doi.org/10.31489/2024M4/119-126
Yeshkeyev, A.R., Yarullina, A.R., & Kassymetova, M.T. (2026). On the Kaiser class of unars in expanded signature. Eurasian Journal of Mathematics, 17(2), 58–69. https://doi.org/10.32523/2077-9879-2026-17-2-58-69
