Independent axiom systems for nearlattices
Joao Araujo, Michael Kinyon
TL;DR
This paper establishes that nearlattices can be characterized by a simple, independent two-axiom system, simplifying their algebraic description and clarifying the dependencies of previous axiom systems.
Contribution
It proves that the variety of nearlattices is 2-based and provides an explicit independent axiom system of two identities.
Findings
The variety of nearlattices is 2-based.
An explicit independent axiom system of two identities is provided.
Original axiom systems are shown to be dependent.
Abstract
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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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Logic, Reasoning, and Knowledge