On the number of countable models of constant and unary predicates expansions of the dense meet-tree theory

Abstract

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 finite realizations. Also, we study the realizations of models over a certain set of formulas based on the Rudin-Keisler preorders on the models.