Title: On transitive subrelations of binary relations
Abstract: 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.
Publication Year: 2011
Publication Date: 2011-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 5
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