On Vaught’s Conjecture and finitely valued MV algebras

Mathematical Logic Quarterly 58 (3):139-152 (2012)

Abstract

We show that the complete first order theory of an MV algebra has equation image 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 equation image and that all ω-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 ω-categorical

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References found in this work

Théories d'Algèbres de Boole Munies d'Idéaux Distingués. II.Alain Touraille - 1990 - Journal of Symbolic Logic 55 (3):1192-1212.
Decidability of Second-Order Theories and Automata on Infinite Trees.[author unknown] - 1972 - Journal of Symbolic Logic 37 (3):618-619.
Introduction to the Special Issue on Vaught's Conjecture.Peter Cholak - 2007 - Notre Dame Journal of Formal Logic 48 (1):1-2.

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