Commutative unital rings elementarily equivalent to prescribed product rings
Logic
2023-07-21 v1
Abstract
The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component structures. Here, by closely related methods, but in the special setting of commutative unital rings, we obtain a kind of converse allowing us to determine in interesting cases, when a commutative unital R is elementarily equivalent to a nontrivial product of a family of commutative unital rings R_i. We use this in the model theoretic analysis of residue rings of models of Peano Arithmetic.
Keywords
Cite
@article{arxiv.2307.10465,
title = {Commutative unital rings elementarily equivalent to prescribed product rings},
author = {Paola D'Aquino and Angus Macintyre},
journal= {arXiv preprint arXiv:2307.10465},
year = {2023}
}