On Vaughts Conjecture and finitely valued MV algebras
We show that the complete first order theory of an MV algebra has 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 and that all ?-categorical complete theories of MV 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 ?-categorical.
finitely valued mv algebra mv algebra vaught's conjecture ?-categoricity free mv algebra msc (2010) 03b50 06d35 03c05.