The logic of the reverse mathematics zoo

TL;DR

This paper explores the logical structure of the reverse mathematics zoo, introducing a tableaux system and natural deduction systems to better understand the implications and nonimplications within this framework.

Contribution

It presents a new formal logical framework, including tableaux and natural deduction systems, for analyzing the reverse mathematics zoo.

Findings

Developed a tableaux system for the reverse mathematics zoo logic

Created natural deduction systems for key fragments of the language

Enhanced understanding of implications and nonimplications in reverse mathematics

Abstract

Building on previous work by Mummert, Saadaoui and Sovine, we study the logic underlying the web of implications and nonimplications which constitute the so called reverse mathematics zoo. We introduce a tableaux system for this logic and natural deduction systems for important fragments of the language.