Equivariant ZFA and the foundations of nominal techniques

TL;DR

This paper introduces a foundational framework for nominal techniques based on an accessible set theory that balances between ZF and FM, highlighting equivariance's theoretical and practical importance.

Contribution

It presents a novel foundational approach to nominal techniques using an intermediate set theory and offers detailed discussions on equivariance's significance.

Findings

Framework is consistent with the Axiom of Choice.

Provides two clear presentations of equivariance.

Enhances understanding of nominal techniques' foundations.

Abstract

We give an accessible presentation to the foundations of nominal techniques, lying between Zermelo-Fraenkel set theory and Fraenkel-Mostowski set theory, and which has several nice properties including being consistent with the Axiom of Choice. We give two presentations of equivariance, accompanied by detailed yet user-friendly discussions of its theoretical significance and practical application.