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December 2011 On transitive subrelations of binary relations
Christopher S. Hardin
J. Symbolic Logic 76(4): 1429-1440 (December 2011). DOI: 10.2178/jsl/1318338858

Abstract

The transitive closure of a binary relation R can be thought of as the best possible approximation of R “from above” by a transitive relation. We consider the question of approximating a relation from below by transitive relations. Our main result is that every thick relation (a relation whose complement contains no infinite chain) on a countable set has a transitive thick subrelation. This allows for a solution to a problem arising from previous work by the author and Alan Taylor. We also exhibit a thick relation on an uncountable set with no transitive thick subrelation.

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Christopher S. Hardin. "On transitive subrelations of binary relations." J. Symbolic Logic 76 (4) 1429 - 1440, December 2011. https://doi.org/10.2178/jsl/1318338858

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1246.03065
MathSciNet: MR2895404
Digital Object Identifier: 10.2178/jsl/1318338858

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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