The Mathematics of Ivo Rosenberg

International audienceThis paper is dedicated to the memory of the distinguished scholar and friend Professor I.G .Rosenberg. We survey some of his most well known and not so known results, as well as present some new ones related to the study of maximal partial clones and their intersections

Semirigid systems of three equivalence relations

International audienc

Semirigid Systems of Equivalence Relations.

International audienceA 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