[FOM] A first-order theory of relations
silver_1 at mindspring.com
Thu May 1 10:37:33 EDT 2008
I have read in a biography of Julia Robinson (I don't know the
author--Feferman?) that in 1973 she "gav[e] a *finite* set of axioms
for number-theoretic functions from which the Peano axioms can be
derived. [my emphasis]
My first question is where can I find this paper *easily*. (It's
listed in a publication I have no access to.)
Next, I don't think I understand what she did, for it's my
impression that there exists *no* finite first-order theory from
which PA can be derived. Could it be that her axioms are not first-
order? Could the axioms be <<too strong>>--possibly implying other
statements that are either false or questionable?
Also, is there something "special" about "number-theoretic
functions" in her axioms, perhaps making the theory second-order
(though second-order PA would do the trick, making it seem
unnecessary to arrive at some other second-order theory)??
I'm familiar with her husband Raphael's Q, which substitutes for the
(infinite) induction schema the simple axiom that says every number
but 0 is a successor, but Q is strictly weaker than PA (though Q can
be used for G's results).
If anyone could provide her axioms or lead me to her paper, I'd very
much appreciate it.
Thanks in advance.
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