[FOM] Justifying SRP?

[WILLIAM TAIT]

On Sep 13, 2014, at 2:18 AM, Rupert McCallum <rupertmccallum at yahoo.com> wrote:

> William Tait wrote an essay that appeared in "The Provenance of Pure Reason" called "Constructing Cardinals from Below" which discussed a set of reflection principles that justify SRP. Unfortunately Peter Koellner later observed that some of the reflection principles he considered were inconsistent. I wrote down my own thoughts in a recent Mathematical Logic Quarterly article about how one might find principled grounds for distinguishing the consistent ones from the inconsistent ones.
> 
> http://onlinelibrary.wiley.com/doi/10.1002/malq.201200015/abstract

Thanks for the announcement, Rupert; I look forward to reading the paper. 

In the interests of immodesty, let me mention that here is a bit of unclarity: I considered reflection principles G^m_n for m, n < omega and used the G^m_2 to derive the existence of m-ineffable cardinals. I also proved the G^m_2 consistent relative to a measurable. Peter showed that they are consistent relative to kappa(omega).

What was unfortunate was certainly not that Peter found the G^m_n inconsistent for n>2, rather it was my proposing them. 

Bill