[FOM] links between nonstandard analysis and formal logic and set theory

Dana Scott dana.scott at cs.cmu.edu
Sun Jan 15 14:40:06 EST 2006

The two books recommended by Alasdair Urquhart in
FOM Digest, Vol 37, Issue 15 sound very interesting.
Here is detailed information from Amazon.com:

      Title: Nonstandard Analysis, Axiomatically
    Authors: Vladimir Kanovei and Michael Reeken
     Series: Springer Monographs in Mathematics
List Price: $109.00
  Hardcover: 408 pages
  Publisher: Springer; 1 edition (October 5, 2004)
       ISBN: 354022243X

      Title: Infinitesimal Analysis
    Authors: E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze
     Series: Mathematics and Its Applications
List Price: $176.00
  Hardcover: 436 pages
  Publisher: Springer; 1 edition (June 30, 2002)
       ISBN: 1402007388

The combined list price of $285.00 is pretty steep, however.
(Some mildly discounted prices are posted at Amazon.)  So
I wonder how students ever afford books anymore.  At 844
combined pages, photocopying at 10 cents a double page is
a temptation -- though of course strictly illegal.  (I'm not
suggesting that!)

So as to make this message more relevant to f.o.m., let
me ask: What work in Reverse Mathematics has been done in
connection with Nonstandard Analysis?

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