@OwoTizusa @JXQNHZr1yUAj5Be 搜到了这一篇CIC in Sets 的paper https://t.co/SCyxixvPro
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@roydanroy @EscardoMartin There are semantics of Coq/Lean (subsets?) in ZFC with universes ^W inaccessibles. Ignoring proof theory questions (that might matter for FFI), that seems enough? Models range from https://t.co/9OxmkwQ7y9 to https://t.co/977NqEGM
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@KamerynJW The upper bound for TT+AC is essentially ZFC plus as many inaccessibles as you have universes. See Benjamin Werner’s “Sets in types, types in sets”, https://t.co/v4rFyrZWFo NB Type theory without LEM/impredicativity is much weaker, see papers b
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RT @plt_abby: * "A type is a set": https://t.co/e3Hbb8g3fv * "A type is a set + an equivalence relation": https://t.co/lVsZTCwb8b * "A ty…