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 $X$ correspond precisely to predicates on $X$. Assuming the law of excluded middle, the boolean-valued functions on $X$ correspond precisely to the subsets of $X$; even in constructive mathematics, they corresond to the decidable subsets of $X$.

Last revised on November 16, 2009 at 08:09:30. See the history of this page for a list of all contributions to it.