Groupoids and the Associative Law Xii. (representable Cardinal Functions)

In this paper we investigate under what conditions is a mapping f of a semigroup S into the class of cardinals representable by a groupoid G and a homomorphism g of G onto S such that ker(g) is the associativity congruence of G and Card(g(x)) = f(x) for every x ∈ S. Abstrakt. V tomto článku vyšetřujeme, za jakých podmı́nek lze zobrazeńı f pologrupy S do tř́ıdy všech kardinálńıch č́ısel reprezentovat grupoidem G a zobrazeńım g : G → S tak, že f(G) = S, ker(g) je kongruence asociativity grupoidu G a Card(g(x)) = f(x) pro všechna x ∈ S.