[FOM] Kreisel on Non-Standard Functional Analysis

[A J Franco de Oliveira]

At 19:35 18-07-2006, rtragesser at mac.com wrote:
>         Did Kreisel overstate the significance of (or mis-state) a
>(supposed) theorem [see below] of NonStandard Functional Analysis,
>viz., that the theorem shows that A. Robinson's "infinitesimals" can
>have dramatic explanatory powers?
>         [[Philosophical interest: If the theorem Kreisel indicated [see
>below] does exist, (...)

I believe the theorem in question is the subject of the paper by 
Bernstein and Robinson "Solution of an invariant subspace problem of 
K T Smith and P R Halmos", Pacific J. of Maths 16(3) (1966) 421-431, 
said problem having been proposed by Aronszajn and Smith "Invariant 
subspaces of completely continuous operators", Ann. Maths. 60
(1964) 345-350. There was much discussion at the time (and a lot of 
"propaganda") about the significance of this theorem for NSA. Note 
that Robinson also spoke of NSA as providing new methods of proof, 
and the said theorem was a case in point.
A whole chapter, with some historical references, is dedicated to the 
subject in A Robert's book "Nonstandard Analysis", Wiley, 1988.
 From sunny Lisbon
ajfo