hairyfigment comments on A quick sketch on how the Curry-Howard Isomorphism kinda appears to connect Algorithmic Information Theory with ordinal logics - LessWrong
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I think the OP means a model of the assertion that arithmetic is inconsistent. It still seems weirdly written, though. (E.g,I don't know how to interpret, "up to any finite ordinal level, standard models of first-order arithmetic".)