FOM: surreal numbers

Stephen G Simpson simpson at
Mon May 24 20:39:04 EDT 1999

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

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