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Oct 14, 2021 at 15:49 history edited FeralX CC BY-SA 4.0
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Oct 14, 2021 at 9:44 comment added Damiano Mazza I suppose you are referring to Harvey Friedman's 1975 paper Equality between functionals, right? Have you looked at the proof to see if there's any obvious way of generalizing it? Personally, I don't know that proof, so I have no idea... What I can say is that, if you do not add any equations in your signature, then the result should still hold, because, from the $\lambda$-calculus viewpoint, you are just introducing constants which behave like free variables. So, unless Friedman's proof only deals with closed terms, it applies.
Oct 13, 2021 at 16:29 history asked FeralX CC BY-SA 4.0