[FOM] Huge cardinals
solovay at gmail.com
Thu Apr 19 19:53:31 EDT 2018
This is in partial response to the following question of Jan Pax: Is it
consistent with ZFC to have a cardinal kappa with the set of HUGE Cardinals
below it forming a stationary set.
We work in Kelly-Morse class-set theory.
Assume that kappa is 2-huge. Then kappa is measurable and there is a normal
measure mu on kappa such that the set of HUGE Cardinals less than kappa has
mu measure one. (A fortiori it is stationary.)
Hence if KM + "there is a 2-huge cardinal" is consistent, so is ZFC plus
"there is a strongly inaccessible cardinal kappa such that the set of HUGE
Cardinals less than kappa is stationary in kappa".
-- Bob Solovay
On Fri, Apr 13, 2018, 9:12 AM <pax0 at seznam.cz> wrote:
> Dear FOMers,
> is it consistent with ZFC to have a cardinal \kappa with
> HUGE cardinals below it being a stationary set?
> Thank you, Jan Pax
> FOM mailing list
> FOM at cs.nyu.edu
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