Chain conditions in dependent groups
Itay Kaplan, Saharon Shelah
TL;DR
This paper investigates chain conditions within groups definable in dependent and strongly dependent theories, providing proofs and counterexamples to clarify their properties.
Contribution
It establishes new results and refutes some assumptions about chain conditions in type definable groups in dependent theories.
Findings
Proves certain chain conditions hold in dependent theories.
Disproves some chain conditions in strongly dependent theories.
Clarifies the limitations of chain conditions in various dependent theories.
Abstract
In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly^{2} dependent theories.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · semigroups and automata theory