Limiting theories of substructures
Samuel M. Corson
TL;DR
This paper introduces the concept of limiting theories, explores conditions under which a structure's theory is the limit of its substructures' theories, and provides a new proof regarding non-finite axiomatizability of certain theories.
Contribution
It defines limiting theories, offers examples, and establishes a sufficient condition for a structure's theory to be the limit of its substructures' theories, along with a new proof of non-finite axiomatizability.
Findings
Introduction of limiting theories concept
Sufficient condition for theory limits from substructures
New proof that certain theories are not finitely axiomatizable
Abstract
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a new proof that theories like that of infinite sets are not finitely axiomatizable.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Advanced Topology and Set Theory