[FOM] A first-order theory of relations

Charles Silver 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.

Charlie Silver

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