ON THE NUMBER OF COUNTABLE MODELS OF CONSTANT AND UNARY PREDICATES EXPANSIONS OF THE DENSE MEET-TREE THEORY
Dauletiyarova A.B. Verbovskiy V.V.
2024Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2024#21Issue 2755 - 770 pp.
In the paper, we investigate Ehrenfeucht theories, that is, theories which have nitely many countable models but which are not countably categorical. More precisely, we count all possible numbers of countable models of the theory DMT of dense meet-trees expanded by several sequences of constants including decreasing ones and by unary predicates with nite realizations. Also, we study the realizations of models over a certain set of formulas based on the Rudin-Keisler preorders on models.
Constant expansion , Ehrenfeucht theory , Rudin-Keisler preorder , small theory , the number of countable models , the number of limit models , the number of prime models
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