FOM: non-foundational foundations?
Stephen G Simpson
simpson at math.psu.edu
Tue Jul 21 15:39:49 EDT 1998
Joe Shipman 9 Jul 1998 16:54:24 writes:
> The intersection of set theory with foundations represents maybe
> 25% of foundations and the majority of set theory, but not enough
> to justify its subsumption.
I don't dispute Joe's percentages. But there is still the question of
why set theory should have its own MSC number independent of logic and
foundations. After all, the non-foundational component of set theory
amounts to a rather small and isolated subject. (Can you imagine
anybody winning a Fields Medal in it?) Moreover, as Andreas Blass 20
Jul 1998 18:47:51 pointed out, other subjects such as recursion theory
and model theory have developed considerably larger non-foundational
components yet are classified as branches of 03, logic and
foundations, for historical reasons.
This raises once again the question that I tried to raise earlier:
Have subjects such as model theory and recursion theory now
transcended their foundational roots, to the point where they should
officially split off and stop masquerading as f.o.m.? The Lempp
correspondence (4 Jun 1998 17:51:15) and the Slaman manifesto (15 Apr
1998 11:48:54) suggest that this may be justified in the case of
recursion theory at least.
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