FOM: surreal numbers

John Pais paisj at
Tue May 25 01:08:09 EDT 1999

Steve, it's a pity that you found it necessary to create that nonexistent
quote below. It disrespects Harry and his book, and the motivation that he
was trying to convey for writing and reading such a book.

I apologize to Harry and John Conway for my part in the confusion that
resulted below.

John Pais

Stephen G Simpson wrote:

> John Pais 24 May 1999 18:50:34
>  > Harry Gonshor's book "Introduction to the Theory of Surreal
>  > Numbers," CUP 1986, ... ``the enrichment of mathematics by the
>  > inclusion of a new structure with interesting properties.''
> But the surreal numbers were *not* a new structure.  They were (and
> are) isomorphic to the saturated real closed ordered fields.  This is
> easy to prove.  See my posting of 21 May 1999 19:59:44.  Correction to
> that posting: I used Tychonoff's theorem, but it would have been more
> appropriate to cite the Rado selection lemma.
> So apparently even as late as 1986, the followers of Conway were not
> aware of the relevant general model-theoretic results and
> constructions, which were first published in the 1950's or early
> 1960's and expounded in model theory textbooks in 1972 (Sacks) and
> 1973 (Chang/Keisler).
> Today, in 1999, are they by now aware of those old model-theoretic
> results and constructions?
> -- Steve

Light = 1/On

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