Jennifer Hyndman (University of Northern British Columbia, Canada), A reader's guide to A Primer of Subquasivariety Lattices

Tue, 30 Nov 2021, 1 pm MST

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 suggests 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.