[FOM] Countable non-standard models of PA

[Alasdair Urquhart]

Allen Hazen is quite right in saying that the
proof that omega + (omega* + omega).eta is the
order type of countable nonstandard models of PA
is remarkably short and sweet.  It's precisely
for this reason that I believe it was known to 
Skolem in the 1930s.  

Although Alonzo Church sits high in my personal
pantheon of logical gods and heros, I don't think
he was infallible.  Also, note that Henkin does not
exactly claim that the characterisation is his own result
(though he also fails to say that it ISN'T).

I looked up Kemeny's paper of 1958, and the proof of
the characterisation has an interesting footnote attached
to it.  It reads as follows:

	9.  This result was found by HENKIN and the author in 1947.
	But a search of the literature indicated that SKOLEM was
	aware of this fact much earlier.

Kemeny and Henkin were both working on their doctorates with Church 
around 1947-48, so it looks as if they were talking about these
things together.  Kemeny's thesis is called: "Type-theory vs.
Set-theory."  Kemeny was also working as Einstein's assistant
as a doctoral student.  He was an interesting guy, who must have known
many of the logicians of that time, but never published much
in logic.

So, my final guess is this.  The result was almost certainly 
known to Skolem in the mid-1930s, and very likely to Tarski
as well.  But it did not appear in print until Henkin's
paper of 1950, and the first journal proof was Kemeny 1958.
The fact that Skolem does not identify it as his own result
in his review of Kemeny is evidence that it is.   In his characteristically
modest fashion, Skolem abstains from claiming a result that he
did not actually publish. 

If any reader of FOM has access to a copy of Henkin's thesis, 
I would be very happy to know what Henkin says of the result there.