FOM: Independent axiomatizations
Sam Buss
sbuss at herbrand.ucsd.edu
Fri Dec 12 13:11:30 EST 1997
Here's an answer to Tait's question on an independent axiomatization
for PA. Since each of I-Sigma-k (k\ge 1) is finitely axiomatized,
we can choose A_k to be a single formula equivalent to I-Sigma-k. Then
take as axioms, the Craig-style set:
A_1, plus all sentences A_i -> A_{i+1} , for i=1,2,3,...
This is easily seen to be an independent set of axioms for PA.
--- Sam Buss
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