Potential Methods for Extending Galvin and Jónsson's Characterization of Distributive Sublattices of Free Lattices

2016/03/16 by Brian T. Chan, Chan, Brian T.
Computer Science · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1603.05124

Abstract

In 1959, F.Galvin and B.Jonsson characterized distributive sublattices of free lattices in their paper. In this paper, I will create new proofs to a portion of Galvin and Jónsson's results. Based on these new proofs, I will explore possible generalizations of F.Galvin and B.Jónsson's work by defining spanning pairs and proving partial results which may help with analysing finite width sublattices of free lattices; and by making some new observations on finitely generated lattices over semidistributive varieties. The work done in this paper may assist in attacking the following long-standing open problem: Which countable lattices are isomorphic to a sublattice of a free lattice?

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