%0 Journal Article
%T Different Similarities
%A Milo£¿ S. Kurili£¿
%J Mathematics
%D 2014
%I arXiv
%X We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities of their self-embedding monoids and intersections of these equivalence relations. In particular, fixing a language $L$ and a cardinal $\kappa$, we consider the interplay between the restrictions of these similarities to the class $Mod _L (\kappa )$ of all $L$-structures of size $\kappa$. It turns out that, concerning the number of different similarities and the shape of the corresponding Hasse diagram, the class of all structures naturally splits into three parts: finite structures, infinite structures of unary languages, and infinite structures of non-unary languages (where all these similarities are different).
%U http://arxiv.org/abs/1412.2073v1