The axiom of choice and model-theoretic structures
J K Truss
TL;DR
This paper explores how the failure of the axiom of choice in set theory relates to specific highly symmetric model-theoretic structures, shedding light on foundational mathematical issues.
Contribution
It establishes new links between the failure of the axiom of choice and the properties of symmetric model-theoretic structures.
Findings
Identifies conditions under which the axiom of choice fails in certain models.
Shows how symmetry properties influence the validity of choice.
Provides insights into the structure of models lacking the axiom of choice.
Abstract
We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Philosophy and History of Science · Philosophy and Theoretical Science