Peter Jipsen (Chapman University), A survey of partially ordered algebras

Tue, 16 Nov 2021, 2 pm MST

In June 2003 I gave a talk at the Annual Meeting of the Association for Symbolic Logic, University of Illinois at Chicago, on “An online database of classes of algebraic structures”. This list of mathematical structures is still on a website at, but is mostly just an alphabetical list of links that point to (sometimes incomplete) axiomatic descriptions of about 300 categories of universal algebras. This past summer I started a project with Bianca Newell to recreate this list of (partially-ordered) algebraic structures as a computable LaTeX document that can be checked for consistency and updated more reliably than the previous collection of webpages. In this talk I will describe this project and recent joint work on partially ordered universal algebras with José Gil-Ferez. In this setting, a partially ordered universal algebra is a poset with finitary operations that are order-preserving or order-reversing in each argument, and congruences are replaced by compatible preorders. Our investigations are based on an unpublished paper from 2004 by Don Pigozzi: Partially ordered varieties and quasivarieties, available here [pdf].