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On sets related to maximal clones

100%

Susanti Y. , Denecke K.

Discussiones Mathematicae - General Algebra and Applications

2012

tom 32

nr 1

101-114

For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study $R_{a̲,b}^{n,k}$ for arbitrary partial order relations, equivalence relations and central relations.

A 2-categorical framework for the syntax and semantics of many-sorted equational logic

51%

Vidal C. , Soliveres Tur J.

tom Vol. 45

37-95

For, not necessarily similar, single-sorted algebras Fujiwara defined, through the concept of family of basic mappingformulas between single-sorted signatures, a notion of morphism which generalizes the ordinary notion of homomorphism between algebras. Subsequently he also defined an equivalence relation, the relation of conjugation, on the families of basic mapping-formulas. In this article we extend the theory of Fujiwara to the, not necessarily similar, many-sorted algebras, by defining the concept of polyderivor between many-sorted signatures under which are subsumed the standard signature morphisms, the derivors of Goguen- Thatcher-Wagner, and the basic mapping-formulas of Fujiwara.