Clones with Nullary Operations

Authors:
Mike Behrisch
Affiliations:
-
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2014

Citing 3
Cited 1

Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory (Springer Monographs in Mathematics)

Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory (Springer Monographs in Mathematics)
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A Short Introduction to Clones

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Abstract

This article discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary sets. By means of two pairs of kernel and closure operators, the relationship between such clones and clones in the traditional sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. Finally, the fundamental theorem characterising Galois closed sets w.r.t. an adjusted version of Pol - Inv as local closures of clones and relational clones, respectively, is proven in the more comprehensive setting.