二阶亨金逻辑中的 AC 和 WO 的独立性,第二部分

Christine Gaßner
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引用次数: 0

摘要

本文关注亨金诠释(HPL)二阶谓词逻辑中的选择公理(AC)和井序定理(WO)。我们考虑了威廉-阿克曼(Wilhelm Ackermann,1935)提出的选择原则,大卫-希尔伯特和阿克曼(David Hilbert and Ackermann,1938)、本杰明-西斯金德(Benjamin Siskind)、保罗-曼科苏(Paolo Mancosu)和斯图尔特-夏皮罗(Stewart Shapiro,2020)也讨论了这一原则。我们的讨论仅限于所谓的二阶亨金-阿瑟结构。在此,我们给出了我们在 2022 年逻辑学术讨论会上提出的关于 WO 独立于 HPL 中所谓阿克曼公理的证明的技术细节。这里使用的大部分定义可以在第一部分的第 1、2 和 3 节中找到。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
AC and the Independence of WO in Second-Order Henkin Logic, Part II
This article concerns with the Axiom of Choice (AC) and the well-ordering theorem (WO) in second-order predicate logic with Henkin interpretation (HPL). We consider a principle of choice introduced by Wilhelm Ackermann (1935) and discussed also by David Hilbert and Ackermann (1938), by G\"unter Asser (1981), and by Benjamin Siskind, Paolo Mancosu, and Stewart Shapiro (2020). Our discussion is restricted to so-called Henkin-Asser structures of second order. Here, we give the technical details of our proof of the independence of WO from the so-called Ackermann axioms in HPL presented at the Colloquium Logicum in 2022. Most of the definitions used here can be found in Sections 1, 2, and 3 in Part I.
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