On distributions of countable models for constant expansions of the dense meet-tree theory. I
https://doi.org/10.55452/1998-6688-2022-19-4-27-33
Abstract
We study all possible constant expansions of the structure of the dense meet-tree ⟨М; <, П⟩ [3]. Here, a dense meet-tree is a lower semilattice without the least and greatest elements. An example of this structure with the constant expansion is a theory that has exactly three pairwise non-isomorphic countable models [6], which is a good example in the context of Ehrenfeucht theories. We study all possible constant expansions of the structure of the dense meet-tree by using a general theory of classification of countable models of complete theories [7], as well as the description of the specificity for the theory of a dense-meet tree, namely, some distributions of countable models of these theories in terms of Rudin– Keisler preorders and distribution functions of numbers of limit models. In this paper, we give a new proof of the theorem that the dense meet-tree theory is countable categorical and complete, which was originally proved by Peretyat’kin. Also, this theory admits quantifier elimination since complete types are forced by a set of quantifier-free formulas, and this leads to the fact that it is decidable
About the Author
A. B. DauletiyarovaKazakhstan
Dauletiyarova Aigerim Baissultanovna, Master, PhD student
040900, Kaskelen
References
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Review
For citations:
Dauletiyarova A.B. On distributions of countable models for constant expansions of the dense meet-tree theory. I. Herald of the Kazakh-British Technical University. 2022;19(4):27-33. https://doi.org/10.55452/1998-6688-2022-19-4-27-33