Questions tagged [consistency]

A system of formal logic is consistent if false is not deducible in the system. (from nLab).

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Unintentionally proven false theorem with type-in-type outside logic and foundations?

We are all familiar with Russell's paradox, and it is known that Per Martin-Löf proved that type-in-type is normalizing and consistent (which is false), by accidentally using an assumption in his meta-...
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Mere propositions and Consistency with Impredicativity, Excluded Middle and Large Elimination

Setup Current Understanding I've recently been trying to learn about the interaction of Impredicative Polymorphism, Large Elimination and Excluded Middle (notably, inconsistency). Notably, this is ...
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