# Mathematical Sciences Research Institute

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# Seminar

An Axiomatization of Products of Rings August 09, 2022 (03:30 PM PDT - 04:15 PM PDT)
Parent Program: Definability, Decidability, and Computability in Number Theory, part 2 MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Paola D'Aquino (Università degli Studi della Campania "Luigi Vanvitelli")
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#### An Axiomatization Of Products Of Rings

Abstract/Media

We axiomatize the class of commutative unital rings which are elementarily equivalent to a non-trivial product of commutative unital connected rings. An example of a ring in this class is $M/nM$ where $M$ is a model of Peano Arithmetic (PA). This is part of a joint work with A.\ Macintyre on the model theoretic analysis of residue rings of models of PA.