I consider some early consistency proofs in the Hilbert School (by Ackermann, von Neumann and Herbrand) for fragments of arithmetic, before Goedel's results. The basic questions I shall try to answer are: What did they prove? Where (in what theory) can one prove what they proved? Which present-day formal theories can 'mimic' those contentual proofs, without violating Goedel's theorem on consistency proofs?
On some early consistency proofs for fragments of arithmetic
BELLOTTI, LUCA
2012-01-01
Abstract
I consider some early consistency proofs in the Hilbert School (by Ackermann, von Neumann and Herbrand) for fragments of arithmetic, before Goedel's results. The basic questions I shall try to answer are: What did they prove? Where (in what theory) can one prove what they proved? Which present-day formal theories can 'mimic' those contentual proofs, without violating Goedel's theorem on consistency proofs?File in questo prodotto:
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