Disciplined Spaces and Centralizer Clone Segments
Věra Trnková, Jiří Sichler · Canadian Journal of Mathematics · 1996
Abstract Our main result implies that for any choice 1 ≤m ≤ n ≤ pof integers there exist finitary algebrasA1andA2that generate the same variety, and such that the initialk-segments of their centralizer clones coincide exactly whenk ≤ m,are isomorphic exactly whenk ≤ nand are elementarily equivalent exactly whenk ≤ p.The proof uses the existence and properties of disciplined topological spaces which we introduce and investigate here.