FOM: Omega logic references

[H. Enderton]

As Allen Hazen points out, the omega-rule trivializes first-order
arithmetic, but comes into its own in second-order arithmetic.
He mentions Orey's completeness theorem (JSL, 1956).  I think
the definitive paper on this was by Grzegorczyk, Mostowski, and 
Ryll-Nardzewski, JSL vol. 23 (1958).  See the review by Feferman,
JSL XXVII 80.  All this seems like ancient history by now, but
it's good stuff.

--Herb Enderton