Methods for demonstrating consistency and their limitations ( 1932 )
نویسندگان
چکیده
‖ The methods that were used to prove the consistency of formalized theories from the finitist standpoint can be surveyed according to the following classification. ‖1. Method of valuation. It has obtained its essential development by Hilbert’s procedure of trial valuation. Using this procedure Ackermann and v. Neumann demonstrated the consistency of number theory—admittedly, under the restrictive condition that the application of the inference from n to (n+ 1) is only allowed to formulas with just free variables. 2. Method of integration. This can only be applied to such domains that are completely mastered mathematically. For those it allows one to give a completely positive answer not only to the question of consistency, but also to those of completeness and decidability. Such domains are in particular:
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