[FOM] some references?

Saeed Salehi saeed_salehi at yahoo.com
Tue Feb 14 11:26:55 EST 2006

Quoting "Harvey Friedman" <friedman at math.ohio-state.edu>:
>> 6. But of course V = L also has a perceived strong 
disadvantage by set theorists, and some other logicians.
Most specifically, a certain set of questions are answered
"the wrong way".
Being a novice on the subject, I would like to ask the
FOMers a favor:
Could somebody please provide references for some of those
set-theoretic questions which are answered the wrong way by
I would also like to see Joe Shipman's proof of the theorem
announced below. 
Quoting "Joe Shipman" <joeshipman at aol.com>:
I recently found a straightforwardly computable necessary 
and sufficient condition for implications between "degree 
axioms" in field theory to be true in all fields.  Let [n]
denote the sentence "all polynomials of degree n have a
root". This is straightforwardly expressible in the
language of field theory, by a sentence whose size is
linear in n (assuming all variables are assigned unit 
size; if we insist on measuring sentence length in terms of
characters in a finite alphabet, then ANY sentence
involving a linear number of variables must be have "size"
at least O(n log n), but this has no relation to the number
of steps necessary in a proof).
Is it published somewhere?
The ongoing discussion is very interesting, and as one
member wrote once "mind-provoking". Just to let you know
that I am one of the excited onlookers too.

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