FOM: Hilbert and Set Theory

Akihiro Kanamori aki at
Tue Oct 14 11:48:41 EDT 1997

  Below is a ps file of the paper, Hilbert and Set Theory, coauthored by
Burton Dreben and myself, recently appearing in Synthese. In it we
try to draw out the influence of Hilbert (and Russell) on Godel,
particularly in his construction of L. We also try to show that
however ``foundational'' logic might have been at the time, Hilbert
made mathematics out of it in pursuit of specific problems and with
specific themes. In particular, we try show how his Finite Basis
Theorem and non-constructive existence proofs resonates with
his later work on decidability through the epsilon-terms. 
  Incidentally, we point out that however the Second Incompleteness
Theorem stands on its own, von Neumann established it independently after
hearing Godel at Konigsberg in 1930 and to the specfic purpose of
point out a difficulty with Ackermann's purported proof of the
the finiteness of the iterated substitution of epsilon-terms, i.e. the 
approach to decidability of number theory of the Hilbert school.
--Aki Kanamori

[ moderator's note: Aki's PS file has been deleted from
this e-mail.  It is available at ]

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