[FOM] Thm of Non-Standard Functional Analysis?

[rtragesser@mac.com]

  Re: Kreisel on Non-Standard Functional Analysis: The
ontological and the epistemic (Haim Gaifman)

   I am grateful for Prof.Gaifman's response.  But I think that my philosophical mutterings misled - what I dearly and urgently hope for is :

Kreisel ascribed a (under his description) very interesting theorem in non-standard functional analysis to A.Robinson, viz.,

"In analysis, nonstandard Hilbert spaces   
...explain the occurrence of a "point" spectrum   
inside continuous spectra in the theory of operators; not unlike the   
 use of the complex plane explains the behavior of power series of the   
real axis..."

I and others are having difficulty in identifying this theorem.  Can anyone help? 

The reference Kreisel gives is to A. Robinson, "On generalized limits and linear  
 functionals," PacJMath 14 (1964) 269-283 [readily available on-line];  
but if the theorem Kreisel is thinking about is there, it must  
require some expert reading between the lines to see it. 


BTW: I think Prof. Gaifman seriously mischaracterizes Godel's Platonism, ascribing to Godel a "Platonism of easy virtue."

Robert Tragesser

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