foundations

# Contents

## Overview

There are various ways to deal with size issues in the foundations of mathematics. All of them involve the notion of universe in one way or another.

In any case, given a universe $U$, we say that a collection is $U$-small if it is in $U$, a collection is $U$-large if it is not in $U$, any subcollection of $U$ is a class, and a subcollection of $U$ is a proper class if it is not a singleton subcollection of $U$.