[FOM] role of large cardinals

meskew at math.uci.edu meskew at math.uci.edu
Wed Sep 21 22:08:25 EDT 2016

I recently wrote the following paragraph-fragment.  I would appreciate any
critiques of the assertions, especially if you disagree with the last
thing starting with "the fact that..."

In contemporary logic, there is a wide-ranging consensus that the
traditional large cardinal axioms are the appropriate measuring-stick for
gauging the logical strength and showing the consistency of any
mathematical statement.  The main reasons for this are their mutual
compatibility, their success in the role so far, and the fact that there
is no known example of a possibly-consistent hypothesis whose strength can
be shown to transcend the large cardinal notions.


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