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4:15 pm
The Provability of Consistency. Sergei Artemov
@ CUNY Grad Center, 7314
The Provability of Consistency. Sergei Artemov
@ CUNY Grad Center, 7314
Nov 4 @ 4:15 pm – 6:15 pm
We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions: 1. Gödel’s internalized consistency formula is the only way to represent consistency. 2. Any contentual reasoning within T internalizes as a formal derivation in T. We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such[...]
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