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arXiv · 1603.05124

Potential Methods for Extending Galvin and J\'onsson's Characterization of Distributive Sublattices of Free Lattices

Brian T. Chan
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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 J\'onsson's results. Based on these new proofs, I will explore possible generalizations of F.Galvin and B.J\'onsson's work by defining \emph{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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Brian T. Chan. 2016-03-16. Potential Methods for Extending Galvin and J\'onsson's Characterization of Distributive Sublattices of Free Lattices. https://arxiv.org/abs/1603.05124

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