FOM: Independent axiomatizations

Sam Buss sbuss at
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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