FOM: non-standard models

Solomon Feferman sf at Csli.Stanford.EDU
Thu Dec 4 02:06:04 EST 1997

Re the history of non-standard models, I would also recommend reading Bob
Vaught's introductory note to a review by Goedel of Skolem's papers of
1933 and 1934 on non-standard models of arithmetic, to be found in Vol.I
of the Goedel *Collected Works*, pp. 376-378.  What is extraordinary, as
Vaught points out, is that Goedel didn't realize that the existence of
non-standard models of the set of all true sentences of arithmetic follows
very simply from his 1930 compactness theorem.  I would add that if he
did, it is even more extraordinary that he didn't point that out in his
review of Skolem.  Of course, Skolem's construction was of independent
interest, as a precursor of ultraproduct constructions. 

Sol Feferman

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