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First-order definable retraction problems for posets and reflexive graphs

Dalmau, V.; Krokhin, A.; Larose, B.

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Authors

V. Dalmau

B. Larose



Abstract

A retraction from a structure P to its substructure Q is a homomorphism from P onto Q that is the identity on Q. We present an algebraic condition which completely characterzies all posets and all reflexive graphs Q such that the class of all posets or reflexive graphs, respectively, that admit a retraction onto Q is first-order definable.

Citation

Dalmau, V., Krokhin, A., & Larose, B. (2007). First-order definable retraction problems for posets and reflexive graphs. Journal of Logic and Computation, 17(1), 31-51. https://doi.org/10.1093/logcom/exl014

Journal Article Type Article
Publication Date Feb 1, 2007
Deposit Date Mar 26, 2010
Publicly Available Date Apr 7, 2010
Journal Journal of Logic and Computation
Print ISSN 0955-792X
Electronic ISSN 1465-363X
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 17
Issue 1
Pages 31-51
DOI https://doi.org/10.1093/logcom/exl014
Keywords Retraction, Homomorphism, Graphs, Posets, First-order definability.
Publisher URL http://logcom.oxfordjournals.org/cgi/reprint/17/1/31

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Copyright Statement
This is a pre-copy-editing author-produced PDF of an article accepted for publication in Journal of logic and computation following peer review. The definitive publisher-authenticated version Dalmau, V. and Krokhin, A. and Larose, B. (2007) 'First-order definable retraction problems for posets and reflexive graphs.', Journal of logic and computation., 17 (1). pp. 31-51 is available online at: http://logcom.oxfordjournals.org/cgi/content/abstract/17/1/31







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