Independent axiom systems for nearlattices

Details Independent axiom systems for nearlattices Independent axiom systems for nearlattices

2010-07-19

arxiv.org/abs/1007.3120v2

Mathematics

Combinatorics

16 pages in 12pt; v2: minor changes suggested by referee, to appear in Czechoslovak Math. J

Scientific paper

A nearlattice is a join semilattice such that every principal filter is a lattice with respect to the induced order. Hickman and later Chajda et al independently showed that nearlattices can be treated as varieties of algebras with a ternary operation satisfying certain axioms. Our main result is that the variety of nearlattices is 2-based, and we exhibit an explicit axiom system of two independent identities. We also show that the original axiom systems of Hickman and of Chajda et al are, respectively, dependent.

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