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2012•Journal of Symbolic LogicRequires access

On countable chains having decidable monadic theory

Alexis Bès, Alexander Rabinovich

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Abstract

Abstract Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

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What this paper is about

Abstract Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

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Available abstract

Abstract Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

Key concepts: Decidability, Countable set, Monadic predicate calculus, Mathematics, Order (exchange), Chain (unit), Discrete mathematics, Order theory

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