The consistency strength of NFUB

TL;DR

This paper establishes that the consistency strength of the NFUB system, a variant of Quine's New Foundations, matches that of ZFC without the Power Set axiom plus the existence of a weakly compact cardinal.

Contribution

It precisely determines the consistency strength of NFUB, linking it to a well-known large cardinal assumption.

Findings

NFUB has the same consistency strength as ZFC minus Power Set plus a weakly compact cardinal.

Provides a complete proof despite being a preliminary draft.

Clarifies the foundational strength of NFUB in set theory.

Abstract

We show that the consistency strength of the system NFUB, a variant of Quine's "New Foundations" recently introduced by Randall Holmes, is precisely that of [ZFC - Power Set] + "There is a weakly compact cardinal''. This is a preliminary draft of the paper. Nevertheless, it contains a complete proof.