Invariance under permutations as a semantic motivation for Stratification

TL;DR

This paper explores how invariance under permutations can serve as a semantic foundation for Quine's NF set theory, by analyzing permutation restrictions and their role in interpreting NF.

Contribution

It introduces a permutation-based semantic framework for NF, starting from minimal restrictions and gradually refining them to interpret the theory.

Findings

Permutation invariance provides a semantic basis for NF

A finite axiomatization of NF is developed from permutation restrictions

Comparisons with earlier approaches highlight the novelty of the method

Abstract

This article examines the notion of invariance under different kinds of permutations in a milieu of a theory of classes and sets, as a semantic motivation for Quine's new foundations "NF". The approach largely depends on interpreting a finite axiomatization of NF beginning from the least restrictions on permutations and then gradually upgrading those restrictions as to enable interpreting NF. Comparisons with earlier works are drawn.