[FOM] Reinhardt cardinals

[meskew at math.uci.edu]

> Can you give a reference for Suzuki's theorem?
>
> Thanks.
>
> -- Bob Solovay


Here is the citation:

"No Elementary Embedding from V into V is Definable from Parameters,"
Akira Suzuki, The Journal of Symbolic Logic , Vol. 64, No. 4 (Dec., 1999),
pp. 1591-1594.

It is also discussed in this recent paper by Hamkins et al:
http://arxiv.org/abs/1106.1951

The idea is simple.  For \phi(x,y,z), let \kappa be least such that for
some z, \phi(x,y,z) defines a Sigma_1 elementary embedding into V with
critical point \kappa.  Pick some witness and apply its embedding, noting
that the above statement is preserved.

Best,
Monroe