[FOM] role of large cardinals

[WILLIAM TAIT]

Weak fragments of second order number theory have consistency strengths (e.g. \epsilon_0, \Gamma, etc.) well below large cardinals. In answer to your question, what about CH?

Best, Bill


> On Sep 21, 2016, at 9:08 PM, meskew at math.uci.edu wrote:
> 
> 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.
> 
> Thanks!
> Monroe
> 
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