Decidable theories of the ordering of natural numbers with unary predicates

Alexander Rabinovich; Wolfgang Thomas

doi:10.1007/11874683_37

Decidable theories of the ordering of natural numbers with unary predicates

Alexander Rabinovich^*, Wolfgang Thomas

^*Corresponding author for this work

School of Computer Science

RWTH Aachen University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

27 Scopus citations

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 language	English
Title of host publication	Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings
Publisher	Springer Verlag
Pages	562-574
Number of pages	13
ISBN (Print)	3540454586, 9783540454588
DOIs	https://doi.org/10.1007/11874683_37
State	Published - 2006
Event	20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL - Szeged, Hungary Duration: 25 Sep 2006 → 29 Sep 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4207 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL
Country/Territory	Hungary
City	Szeged
Period	25/09/06 → 29/09/06

Access to Document

10.1007/11874683_37

Cite this

Rabinovich, A., & Thomas, W. (2006). Decidable theories of the ordering of natural numbers with unary predicates. In Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings (pp. 562-574). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4207 LNCS). Springer Verlag. https://doi.org/10.1007/11874683_37

Rabinovich, Alexander ; Thomas, Wolfgang. / Decidable theories of the ordering of natural numbers with unary predicates. Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings. Springer Verlag, 2006. pp. 562-574 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Rabinovich, A & Thomas, W 2006, Decidable theories of the ordering of natural numbers with unary predicates. in Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4207 LNCS, Springer Verlag, pp. 562-574, 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Szeged, Hungary, 25/09/06. https://doi.org/10.1007/11874683_37

Decidable theories of the ordering of natural numbers with unary predicates. / Rabinovich, Alexander; Thomas, Wolfgang.
Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings. Springer Verlag, 2006. p. 562-574 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4207 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Rabinovich A, Thomas W. Decidable theories of the ordering of natural numbers with unary predicates. In Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings. Springer Verlag. 2006. p. 562-574. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11874683_37

Decidable theories of the ordering of natural numbers with unary predicates

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