# nLab first-order set theory

Contents

foundations

## Removing axioms

#### 2-category theory

2-category theory

# Contents

## Idea

First-order set theory is structural set theory with a notion of families of sets, which are functors $F:I \rightarrow Set$ from an index set $I$ to Set, the groupoid of sets. This is similar to first-order logic which has a notion of family of propositions or predicates. This is in contrast to zeroth-order set theory, which do not have a concept of family of sets defined, and in higher-order set theory, which have families of families in addition to families of sets.

The syntactic category of a first-order set theory should be a (2,1)-category with additional structure, although at this moment it is unclear exactly what (2,1)-category it would be.

Created on March 3, 2021 at 00:10:32. See the history of this page for a list of all contributions to it.