Jordan DuBeau (University of Colorado), Jónsson Jónsson-Tarski algebras

Tue, 22 February 2022, 1 pm MST

For an infinite algebra $J$ in a countable algebraic language, we say $J$ is Jónsson if it has no proper subalgebra of the same cardinality as $J$. This talk explores Jónsson algebras in a particular variety: the variety of Jónsson-Tarski algebras. When a Jónsson algebra of size $\aleph_1$ was constructed in this variety, it showed that minimal varieties can contain uncountable Jónsson algebras. We will describe that construction and two further results, demonstrating exactly which cardinalities are possible for Jónsson Jónsson-Tarski algebras, and how many pairwise nonisomorphic Jónsson Jónsson-Tarski algebras exist. We discuss implications for other varieties and Jónsson algebras in general.

[slides] [preprint] [video]