On Vaught’s Conjecture and finitely valued MV algebras

摘要

We show that the complete first order theory of an MV algebra has 2~(N_0) countable models unless the MV algebra is finitely valued. So, Vaught’s Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are 2~(N_0) and that all ω- categorical complete theories ofMV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators of any locally finite variety of MV algebras is ω-categorical.