Submission date: 27 December 2021

Abstract:

We classify countable Boolean rings with finitely many distinguished ideals whose elementary theory is countably categorical. This extends the work of Macintyre and Rosenstein and subsequent authors on countably categorical Boolean algebras with finitely many distinguished ideals. Following Pierce, our classification takes a topological approach using the language of PO systems (partially ordered sets with a distinguished subset) and topological Boolean algebras. We discuss how our findings link with previous results, but the paper is otherwise self-contained.

Mathematics Subject Classification: 06E15 (Primary) 06A06 (Secondary)

Keywords and phrases:

Full text arXiv 2112.13825: pdf, ps.