Decidable theories of the ordering of natural numbers with unary predicates

Alexander Rabinovich, Wolfgang Thomas

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order logic. Building on the modeltheoretic composition method of Shelah, we give two characterizations of the decidable theories of this form, in terms of effectiveness conditions on two types of "homogeneous sets". We discuss the significance of these characterizations, show that the first-order theory of successor with extra predicates is not covered by this approach, and indicate how analogous results are obtained in the semigroup theoretic and the automata theoretic framework.

Original languageEnglish
Title of host publicationComputer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings
PublisherSpringer Verlag
Pages562-574
Number of pages13
ISBN (Print)3540454586, 9783540454588
DOIs
StatePublished - 2006
Event20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL - Szeged, Hungary
Duration: 25 Sep 200629 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4207 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL
Country/TerritoryHungary
CitySzeged
Period25/09/0629/09/06

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