nLab boolean-valued function

A boolean-valued function is a function from any set to the boolean domain {,}\{\bot, \top\}.

In classical logic, the definable boolean-valued functions on a type XX correspond precisely to predicates on XX. Assuming the law of excluded middle, the boolean-valued functions on XX correspond precisely to the subsets of XX; even in constructive mathematics, they corresond to the decidable subsets of XX.

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