Representations of Symmetric Implication Algebras as Multicubes

Details Representations of Symmetric Implication Algebras as Multicubes Representations of Symmetric Implication Algebras as Multicubes

2009-02-05

arxiv.org/abs/0902.0993v1

Mathematics

Combinatorics

25 pages

Scientific paper

We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to cubic implication algebras and provide a representation of these algebras as subalgebras of a product of a cubic implication algebra and an implication algebra. We then show that every symmetric implication algebra is covered by a locally symmetric implication algebra.

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