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Abstract
本文重新讨论了逻辑律和集合论。本文基于同一性的概念，提出了增强 的逻辑律，并简洁地解决了罗素悖论和康托尔悖论。重新审视了ZFC公理系统，其中的有关集合存在的公理合并成概括公理，而正则公理被证明，降为 定理。增强了外延公理，从而解决希尔伯特旅馆悖论和巴拿赫-塔斯基悖论， 消除了对选择公理的疑虑并将之保留。 重新构建的集合论公理有三条:概括 公理，选择公理，外延公理，恢复了康托尔集合论的简洁和优雅。
Abstract
This paper revisits the laws of logic and set theory. Based on the concept of identity, enhanced laws of logic are proposed, which neatly solve Russell’s Paradox and Cantor’s Paradox. The ZFC axiomatic system is reexamined, with the axioms pertaining to the existence of a particular set consolidated into the Axiom of Comprehension, while the Axiom of Regularity is downgraded to a theorem through proof. The Axiom of Extensionality is enhanced to solve the Hilbert’s Hotel Paradox and the Banach-Tarski Paradox, alleviating doubts regarding the Axiom of Choice. The restructured axiomatic system of set theory comprises three fundamental axioms: the Axiom of Comprehension, the Axiom of Choice, and the Axiom of Extensionality, thereby restoring the elegance of Cantor’s set theory.
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发表于 2024-10-5 04:30:28
