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Semirigid Systems of Equivalence Relations.

Abstract : A system \\textbackslashmathcal M\ of equivalence relations on a set \E\ is \textbackslashemph\semirigid\ if only the identity and constant functions preserve all members of \\textbackslashmathcal M\. We construct semirigid systems of three equivalence relations. Our construction leads to the examples given by Z\textbackslash'adori in 1983 and to many others and also extends to some infinite cardinalities. As a consequence, we show that on every set of at most continuum cardinality distinct from \2\ and \4\ there exists a semirigid system of three equivalence relations.
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https://hal.univ-reunion.fr/hal-01188005
Contributor : Nicolas Alarcon <>
Submitted on : Friday, August 28, 2015 - 12:59:26 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:15 PM

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  • HAL Id : hal-01188005, version 1

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Christian Delhommé, Masahiro Miyakawa, Maurice Pouzet, Ivo G. Rosenberg, Hisayuki Tatsumi. Semirigid Systems of Equivalence Relations.. IEEE 42nd International Symposium on Multiple-Valued Logic ISMVL-2012, May 2012, Victoria, Canada. pp.293--298. ⟨hal-01188005⟩

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