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• W2948179623 abstract "In this paper, we describe the formalization of the axiom of choice and several of its famous equivalent theorems in Morse-Kelley set theory. These theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal principle, Zermelo's postulate, Zorn's lemma and the well-ordering theorem. We prove the above theorems by the axiom of choice in turn, and finally prove the axiom of choice by Zermelo's postulate and the well-ordering theorem, thus completing the cyclic proof of equivalence between them. The proofs are checked formally using the Coq proof assistant in which Morse-Kelley set theory is formalized. 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." @default.
• W2948179623 created "2019-06-14" @default.
• W2948179623 creator A5075794643 @default.
• W2948179623 creator A5086819750 @default.
• W2948179623 date "2019-06-10" @default.
• W2948179623 modified "2023-09-27" @default.
• W2948179623 title "Formalization of the Axiom of Choice and its Equivalent Theorems" @default.
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