[FOM] Justifying SRP?

Harvey Friedman hmflogic at gmail.com
Fri Sep 12 13:54:05 EDT 2014

One of the more well known senior Fields Medalists (senior even by my
standards) has gotten interested in the recent Pi01 independence.
These are provable using the subtle cardinal hierarchy but not with
less. In fact, provably equivalent to the consistency thereof.

The subtle cardinal hierarchy is the same as the ineffable cardinal
hierarchy, and this is also the same as the SRP hierarchy - each
cofinal in each other.  Recall that SRP stands for "stationary Ramsey
property", which asserts that every partition of the k-tuples into two
pieces has a stationary homogenous set.

He writes me "why should I believe that there is a subtle cardinal (or
k-subtle cardinal), or even that it is consistent?"

I already answered that it is my business to get the issue joined by
proving equivalence with Con(SRP). I said I would get back to him
about the so called "arguments" for SRP and Con(SRP).

Now how should I respond for a senior Fields Medalist in core
mathematics who clearly is a combination of dubious/not knowledgeable
about higher set theory?

If the cardinals were somewhat smaller, than I would just give the
second order reflection story as my best shot - with a class


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