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Groupoids and the associative law. XII: Representable cardinal functions. (English) Zbl 0904.20049

[For part IX of this series see ibid. 38, No. 1, 39-52 (1997; Zbl 0889.20042).]
In this paper is studied 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 \(\text{Card}(g^{-1}(x))=f(x)\) for every \(x\in S\).

MSC:

20N02 Sets with a single binary operation (groupoids)

Citations:

Zbl 0889.20042
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