TL;DR
This paper investigates the properties of neat atom structures, showing that the class of such structures is not elementary, which has implications for algebraic logic and model theory.
Contribution
It demonstrates that the class of neat atom structures cannot be characterized by a first-order theory, revealing limitations in their logical definability.
Findings
The class of neat atom structures is not elementary.
Neat atom structures do not form a first-order definable class.
Implications for algebraic logic and model theory.
Abstract
An atom structure is neat if there an algebra based on this atom structure in Nr_nCA_{\omega}. We show that this class is not elementary
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Finite Group Theory Research