[FOM] Consistency of formal systems

Torkel Franzen torkel at sm.luth.se
Sat Jun 14 07:31:49 EDT 2003

Bill Tait says:

 >Turing, Feferman and Fenstad have 
 >written on such hierarchies of theories; but I don't remember the 
 >details. I think that Feferman gave a bound on how high such a 
 >hierarchy could go and then Fenstad improved on it (?)

 The proof in Fenstad's JSL article was incorrect. I haven't seen
any specification of where the error lies.

  About the argument at issue:

     Continue this procedure transfinite inductively to reach the
     cardinality of continuum.

  This makes no obvious sense.

Torkel Franzen

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