Set Theory and Logic

   

Refutation of Formalization of Axiom of Choice and Equivalent Theorems Using the Coq Tool

Authors: Colin James III

We evaluate two definitions for maximum and minimal set membership, for the nesting of sets, and the equivalence relations of axiom of choice, Tukey’s lemma, Hausdorff maximal principle, maximal principle, Zermelo’s postulate, Zorn’s lemma, well-ordering theorem. None is tautologous, refuting the claims. The authors conclude: “The whole process of formal proof demonstrates that the Coq-based machine proving of mathematics theorem is highly reliable and rigorous. The formal work of this paper is enough for most applications, especially in set theory, topology and algebra.” We refute those assertions based on the non-bivalent performance of the Coq proof assistant. Therefore, these formalizations and methodology render a non tautologous fragment of the universal logic VŁ4.

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[v1] 2019-06-23 09:18:35

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