From: Richard Carr <carr@math.columbia.edu>
Newsgroups: sci.math
Subject: Re: Regular Limit Cardinals
Date: Fri, 11 Dec 1998 17:38:07 -0500

On Fri, 11 Dec 1998, Arthur L. Rubin wrote:

:Date: Fri, 11 Dec 1998 11:13:22 +0700
:From: Arthur L. Rubin <216-5888@mcimail.com>
:Newsgroups: sci.math
:Subject: Re: Regular Limit Cardinals
:
:Clive Tooth wrote:
:> 
:> Richard Carr wrote:
:> 
:> > Such cardinals are generally called weakly inaccessible. If you can
:> > prove
:> > that they do not exist (on the basis of ZFC) then you should, if
:> > there's
:> > any justice on the committee, win a Fields Medal.
:> > This would be an amazing result.
:> 
:> the thoughts of mathematicians scroll across my screenday after day I
:> gaze at them
:> such cardigans are generally called  weekly inaccessible
:> open mouthed
:> amazed
:> stunned
:> such cardioids are generally called wiggly but ineffable
:
:Actually, there is a property of cardinals called "ineffable" --
:but I'm not sure how to describe it at the moment at the
:level of expertise of this newsgroup.
:
:--  
:Arthur L. Rubin  216-5888@mcimail.com
:

kappa is ineffable iff kappa is regular and  uncountable and for any
sequence A_alpha (alpha<kappa) with A_alpha a subset of alpha, there is a
stationary subset S of kappa (that is a set S which meets every subset of
kappa that is closed and unbounded in kappa with respect to the ordr
topology on kappa) such that if alpha and beta are in S, with alpha<beta
then A_alpha is the intersection of A_beta with alpha.