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Journal of Logic and Computation Advance Access originally published online on August 23, 2006
Journal of Logic and Computation 2007 17(1):31-51; doi:10.1093/logcom/exl014
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

First-order Definable Retraction Problems for Posets and Reflexive Graphs*

Víctor Dalmau

Department of Technology, University Pompeu Fabra, Barcelona 08003, Spain. E-mail: victor.dalmau{at}upf.edu

Andrei Krokhin

Department of Computer Science, University of Durham, Durham, DH1 3LE, UK. E-mail: andrei.krokhin{at}durham.ac.uk

Benoit Larose

Department of Mathematics and Statistics, Concordia University, Montréal, Canada H3G 1M8. Email: larose{at}mathstat.concordia.ca

Received 14 November 2005.


  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.

Keywords: Retraction; homomorphism; graphs; posets; first-order definability


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