Decidable expansions of labelled linear orderings

Authors:
Alexis Bès;Alexander Rabinovich
Affiliations:
University of Paris-Est Créteil, LACL;Tel-Aviv University, The Blavatnik School of Computer Science
Venue:
Fields of logic and computation
Year:
2010

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Abstract

Let M = (A, P) where (A, P denotes a finite sequence of monadic predicates on A. We show that if A contains an interval of order type ω or -ω, and the monadic second-order theory of M is decidable, then there exists a non-trivial expansion M′ of M by a monadic predicate such that the monadic second-order theory of M′ is still decidable.