Submission date: 22 April 2020

Abstract:

We ask some questions and make some observations about the (complete) theory T (∞, V) of free algebras in V on infinitely many generators, where V is a variety in the sense of universal algebra. We focus on the case T(∞, R) where V is the variety of R-modules (R a ring). Building on work in Kucera-Pillay we characterize when all models of T(∞, R) are free, projective, flat, as well as when T(∞,R) is categorical in a higher power.
We also give a counterexample to a conjecture of Tarski that we heard about from John Baldwin.

Mathematics Subject Classification: 03C45, 03C60, 03C05, 16D40

Keywords and phrases:

Full text arXiv 2004.10351: pdf, ps.