On countable chains having decidable monadic theory
Alexis Bès and Alexander Rabinovich
Source: J. Symbolic Logic Volume 77, Issue 2
(2012), 593-608.
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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