FOM: a correction; Martin/Steel/Woodin analogy?
Stephen G Simpson
simpson at math.psu.edu
Sat Sep 5 10:44:24 EDT 1998
In my previous posting, I said:
> And if anyone is taking Shoenfield seriously, it will surely be
> worthwhile to elaborate on:
> > 7. Progress is sufficiently clear so that lack of formal criteria for
> > progress is not serious nor is it an impediment to progress.
> > 8. Some formal criteria for progress can be given, but is not as important
> > as continued progress.
Instead of "taking Shoenfield seriously", I should have said "taking
Shoenfield's comments on formalization seriously". This is what I
intended. My intention was probably clear from the context, but
I don't want to leave any doubt.
By the way, I still don't understand Shoenfield's suggestion to extend
Harvey's independence results in analogy to the Martin/Steel/Woodin
theorem concerning projective determinacy. Could somebody please tell
me, did Shoenfield have a specific conjecture in mind, or even a
glimmer of one? Perhaps he didn't, and his only purpose was to, as he
said, "encourage Harvey" by dangling the Karp Prize in front of him.
But if Shoenfield did have a specific f.o.m. conjecture in mind, I'd
like to know what it was.
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