# nLab higher-order logic

foundations

## Foundational axioms

foundational axiom

# Contents

## Idea

A higher-order logic is any logic which features higher-order predicates, which are predicates of predicates or of operations.

If we think of a predicate as a function to truth values, then a higher-order predicate is a function on a power set or a function set.

Higher-order intuitionistic logic is often identified with the internal logic of a topos.

Revised on March 20, 2013 18:59:47 by Urs Schreiber (82.169.65.155)