Normal Jonsson theories and their Kaiser classes
Yeshkeyev A.R. Kassymetova M.T. Mussina N.M.
2025E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2025#117Issue 1199 - 210 pp.
We present results concerning new notion connected with the study of Jonsson theories. The new notion is a Kaiser class of models for arbitrary Jonsson theories. All results are obtained within the framework of the normality of the considered Jonsson theory. Additionally, we describe the properties of lattices formed by perfect fragments of a fixed Jonsson theory and their relationship with the #-companion of these fragments. The results we obtained are the model-theoretic properties of the #-companion of a normal perfect Jonsson fragment. Furthermore, we establish necessary and sufficient conditions for a normal Jonsson theory to be perfect, expressed in terms of the lattices of existential formulas.
almost Jonsson set , Jonsson set , Jonsson theory , normality , semantic model
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Institute of Applied Mathematics, Karaganda Buketov University, Karaganda, Kazakhstan
Institute of Applied Mathematics
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