[FOM] Inconsistency of Inaccessibility

[MartDowd at aol.com]

In a message dated 10/26/2011 7:32:44 A.M. Pacific Daylight Time,  
JoeShipman at aol.com writes:

What is the logically and ontologically simplest meaningful statement  
whose truth depends on the existence of measurable cardinals and not simply on  
the arithmetical consequences of measurable cardinals such as their  
consistency?

 
That's a good question.  From a quick scan of Jech, I would say the  
existence of elementary embeddings,
and the existence of Ramsey cardinals, are good examples.  It is  
interesting to note that many relative
consistency results use "core model theory", which is model theory, and  
requires only consistency, not exixtence.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20111026/5f5b406e/attachment.html>