AC and the Independence of the Law of Trichotomy in Second-Order Henkin Logic

2024/10/30 by Christine Gaßner, Gaßner, Christine
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2410.23276

openalex publication_date 2024/10/30 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the set HAC of 1-1 Ackermann axioms of choice in second-order predicate logic with Henkin interpretation (HPL). To answer a question posed by Michael Rathjen, we restrict the proof that the basic Fraenkel model of second order is a model of all n-m Ackermann axioms to the case where the Ackermann axioms are in HAC. In the second part, we show the independence of Hartogs' version of the law of trichotomy (TR) from HAC in HPL. A generalization of the latter proof implies the independence of TR from all Ackermann axioms in HPL. We conclude the paper with an open problem.

Related

• AC and the Independence of WO in Second-Order Henkin Logic, Part I
• AC and the Independence of WO in Second-Order Henkin Logic, Part II
• Relationships between Principles of Choice in Second-Order Henkin Structures
• Permutation Models of Second Order
• Generalizing Hartogs' Trichotomy Theorem