Semirigid Systems of Three Equivalence Relations
Christian Delhommé, Masahiro Miyakawa, Maurice Pouzet, Ivo G. Rosenberg and Hisayuki Tatsumi
A system ? of equivalence relations on a set E is semirigid if only the identity and constant functions preserve all members of ?. We construct semirigid systems of three equivalence relations. Our construction leads to the examples given by Zádori 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.
Keywords: Clones, rigidity, semirigidity, equivalence relations, 3-nets, latin squares, quasigroups
2000 Mathematics Subject Classification. 94D05, 03B50.