🚀 go-pugleaf

---Please reply by e-mail or followup to 
fj.sci.math or to sci.logic, either in 
English or in Japanese.  TeX and LaTeX 
commands are okay, but I prefer an 
informal discussion, leaving 
technicalities to a reference.

Can somebody out there tell me as intuitively as possible how to prove that
a proof is free from Zorn's lemma?  Is it difficult to prove that?  Give
the best reference that is accessible to an entering _American_ (I mean,
not Japanese) graduate student of mathematics---which means that she is not
familier with axiomatic set theory.  (However, you can assume the inquirer
has some familiarity with elementary recursion theory and first-order
logic, though it may be irrelevant.)

--
{Motivation}.  In a paper in social science that I'm writing, I proved a
proposition that a "social rule" exists that satisfies certain conditions. 
Previously, similar propositions were proved using Zorn's lemma. 
Unfortunately, asserting existence of a certain social rule based on the
Zorn's lemma is very unsatisfactory for obvious reasons (how do you
construct the rule?, for example).  In my proof, I believe that I didn't
use Zorn's lemma.  (Don't be astonished---something that is essential to
the proof is assumed to be countable, unlike other papers.)  

However, I noticed that I cannot really assert that I did not use Zorn's
lemma.
After all, I never learnt how to _prove_ that Zorn's lemma is _not_ used in
a proof; I only learned how to use the lemma.

Reiju
-- 
\\                                          //
  H. Reiju Mihara (miha0008@gold.tc.umn.edu) 
  is a name    of some sort 
                               of individual
//                                          \\