A Reader's Guide to A Primer of Subquasivariety Lattices

Abstract: Birkhoff and Mal'cev independently posed the problem: Describe all subquasivariety lattices. Nurakunov in 2009 showed that there are many unreasonable subquasivariety lattices where unreasonable means there is no algorithm to determine if a particular finite lattice is a sublattice. This sugests refinements of the original question are needed.

A subquasvariety lattice has a natural equaclosure operator. Adaricheva and Gorbunov in 1989 defined an equaclosure operator abstractly as having the properties that are known to hold in a natural equaclosure operator.

The soon-to-be-published book, A Primer of Quasivariety Lattices by Kira Adaricheva, Jennifer Hyndman, JB Nation, and Joy Nishida, refines the abstract definition of equaclosure operator and provides some answers to the refined question: When is a lattice with an equaclosure operator representable by a subquasivariety lattice and the natural equaclosure operator. This presentation explores some of this new approach.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.