On distributions of countable models for constant expansions of the dense meet-tree theory. I

We study all possible constant expansions of the structure dense meet-tree ⟨М; <, П⟩ [3]. Here, a is lower semilattice without least and greatest elements. An example this with expansion theory that has exactly three pairwise non-isomorphic countable models [6], which good in context Ehrenfeucht theories. by using general classification complete theories [7], as well description specificity for dense-meet tree, namely, some distributions these terms Rudin– Keisler preorders distribution functions numbers limit models. In paper, we give new proof theorem categorical complete, was originally proved Peretyat’kin. Also, admits quantifier elimination since types are forced set quantifier-free formulas, leads to fact it decidable