nLab
first-order set theory

Contents

Context

Foundations

2-category theory

Contents

Idea

First-order set theory is structural set theory with a notion of families of sets, which are functors F:ISetF:I \rightarrow Set from an index set II 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.