AC and the Independence of WO in Second-Order Henkin Logic, Part II

2024/09/17 by Gaßner, Christine
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2409.11126

Abstract

This article is concerned 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 Günter 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 of Part I.

Related

• AC and the Independence of WO in Second-Order Henkin Logic, Part I
• Relationships between Principles of Choice in Second-Order Henkin Structures
• AC and the Independence of the Law of Trichotomy in Second-Order Henkin Logic
• Permutation Models of Second Order
• Formalization of the Axiom of Choice and its Equivalent Theorems