FOM: Strong Axioms of Infinity in NFU

[Joe Shipman]

I'd like to recommend M. Randall Holmes's paper "Strong Axioms of
Infinity in NFU" ( http://math.idbsu.edu/~holmes/holmes/nfum.ps ), which
reviews work by Holmes and Solovay on natural extensions of NFU that
entail consistency of large cardinals (a progression of theories
culminating in Holmes's "NFUM" whose strength is just short of
measurability).

To my mind, the biggest advantage of NFU lies right here -- because the
strong extensions are much more naturally motivated than extensions of
ZFC by comparable cardinals (n-Mahlos, weakly compacts, measurables).

-- Joe Shipman