Semirigid systems of three equivalence relations
| Autor: | Delhommé, Christian, Miyakawa, Masahiro, Pouzet, Maurice, Rosenberg, Ivo G., Tatsumi, Hisayuki |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 23 pages, 3 figures. Submitted, results presented to ISMVL-2012 |
| Databáze: | arXiv |
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