FOM: Simplicity, Calculus, Need for new axioms JSHIPMAN at
Fri Nov 14 16:18:19 EST 1997

1) I like Harvey's plan of finding the simplest language for CH.  Smullyan did
the exact same kind of thing thirty years ago when he constructed a very simple
language "SELF" which exhibited genuine incompleteness phenomena.  I think
Manin did something similar for forcing ~CH in his wonderful text "A Course in
Mathematical Logic" (which I recommend very highly).
2) Thanks to David Ross for his example.  OK, nonstandard analysts: is the
theorem "continuous function attains a max on closed interval" true in any
concrete models of infinitesimals such as the surreals or the surreals up to
ordinal stage alpha for some infinite alpha?  If so, great!  If not, how hard
is it to prove that it still holds for the subfield of standard reals without
simply duplicating the epsilonics of standard analysis?
3) MacOS used to be better than Windows but the gap has been closing rapidly
4) I'll let Harvey answer most of Feferman (as summarized by Franzen) but wish
to strongly disagree with the claim that PA can formalize physics (even in an
"impractical" sense), given the current state of physics--more later! -J Shipman

More information about the FOM mailing list