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.
[video]