by Sam Eisenstat 17 days ago | link | parent 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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