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by Alex Appel 18 days ago | link | parent

Caught a flaw with this proposal in the currently stated form, though it is probably patchable.

When unpacking a proof, at some point the sentence \(\Box_{1}\phi\) will be reached as a conclusion, which is a false statement.



by Sam Eisenstat 17 days ago | link

I misunderstood your proposal, but you don’t need to do this work to get what you want. You can just take each sentence \(\square_n \phi \to \phi\) as an axiom, but declare that this axiom takes \(n\) symbols to invoke. This could be done by changing the notion of length of a proof, or by taking axioms \(\psi_{\phi,n} \to (\square_n \phi \to \phi)\) and \(\psi_{\phi,n}\) with \(\psi_{\phi,n}\) very long.

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