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.

Revised on November 16, 2009 08:09:30 by Toby Bartels (173.60.119.197)