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On countable chains having decidable monadic theory

Published online by Cambridge University Press:  12 March 2014

Alexis Bés  and
Alexander Rabinovich
Alexis Bés
Affiliation:
University of Paris-Est Créteil, Laboratoire d'Algorithmique, Complexité et Logique, Faculté des Sciences et Technologie, 61 Avenue du Général de Gaulle, 94010 Créteil, France, E-mail: bes@u-pec.fr
Alexander Rabinovich
Affiliation:
The Blavatnik School of Computer Science, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel, E-mail: rabinoa@post.tau.ac.il
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 593 - 608
Copyright
Copyright © Association for Symbolic Logic 2012

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