New equivalences to axioms weaker than AC in topology
Daniel de-la-Concepci\'on
TL;DR
This paper establishes new equivalences between topological statements and weaker axioms than the Axiom of Choice, utilizing anti-properties and computer-verified proofs.
Contribution
It introduces novel equivalences involving weaker axioms than AC in topology, verified with the Isabelle/Isar theorem prover.
Findings
New equivalences between topological statements and weaker axioms than AC
Use of anti-properties in establishing these equivalences
Computer-verified proofs available in isarmathlib
Abstract
In this work, new equivalences of topological statements and weaker axioms than are proven. This equivalences include the use of anti-properties. All this equivalences have been checked with a computer using the theorem proving system Isabelle/Isar and are available at the isarmathlib repository.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Logic, Reasoning, and Knowledge