FOM: background on incompleteness I
Stephen G Simpson
simpson at math.psu.edu
Sat Sep 5 09:34:18 EDT 1998
Harvey, your posting "background on incompleteness I" is excellent and
I am looking forward to parts II, III, .... Many FOM subscribers
already understand the general thrust of your research in this area,
but a fuller statement may help clarify some points.
For instance, many people may benefit from an elaboration of your
points about the incremental nature of progress in this area:
> 4. Progress has been far more incremental than the early work of Godel and
> 5. Progress will continue to be incremental.
> 6. Progress is already more than sufficient to expect continuing long term
> success of the program.
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.
> 9. Progress has been, and will continue to be informally tested by
> interaction with mathematicians outside f.o.m. and mathematical logic.
And I need you to explain this one:
> 10. There are prototypical results (unfortunately, demonstrably false)
> which indicate anticipated future stages of progress.
And of course everybody is eager for your upcoming announcements:
> 11. Over the next couple of months I will make some announcements which
> represent a next stage of progress.
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