2018-03-21: Jamie Gabbay (Heriot-Watt)

Tue, 14 Oct 2025 16:51:42 +0000

Jamie Gabbay (Heriot-Watt)

Equivariant ZFA and the foundations of nominal techniques

Abstract

The sets foundations of nominal techniques are usually taken to be Fraenkel-Mostowski set theory (which is ZFA + a finite support property). I will argue that in many situations, a new foundation which I call Equivariant ZFA (EZFA) may be a better choice, because you can do everything in EZFA that you can do in FM and furthermore EZFA with Choice (EZFAC) is consistent whereas FM with Choice is not.

I will define EZFA and how it interacts with Choice.

I will prove that EZFA is equivalent to ZFA.

I will then prove that EZFA is not equivalent to ZFA.

I will explain why I think EZFA(C) may be useful, why my last three papers were actually written in EZFAC, and finally I will discuss the implications this may have for mathematical foundations in general.

2018-03-21 15:00:00 UTC
LT1415