# Semirigid systems of three equivalence relations

Abstract : A system $\mathcal M$ of equivalence relations on a set $E$ is \emph{semirigid} if only the identity and constant functions preserve all members of $\mathcal M$. We construct semirigid systems of three equivalence relations. Our construction leads to the examples given by Z\'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.
Type de document :
Pré-publication, Document de travail
23 pages, 3 figures. Submitted, results presented to ISMVL-2012. 2015
Domaine :
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http://hal.univ-reunion.fr/hal-01477264
Contributeur : Réunion Univ <>
Soumis le : lundi 27 février 2017 - 11:34:06
Dernière modification le : jeudi 11 janvier 2018 - 06:21:19

### Identifiants

• HAL Id : hal-01477264, version 1
• ARXIV : 1505.02955

### Citation

Christian Delhommé, Masahiro Miyakawa, Maurice Pouzet, Ivo G. Rosenberg, Hisayuki Tatsumi. Semirigid systems of three equivalence relations. 23 pages, 3 figures. Submitted, results presented to ISMVL-2012. 2015. 〈hal-01477264〉

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