nLab three-sorted set theory

Three-sorted set theory

Context

Foundations

foundations

The basis of it all

 Set theory

set theory

Foundational axioms

foundational axiom

Removing axioms

Three-sorted set theory

 Overview

Three-sorted set theories are set theories with three different sorts, representing sets, elements, and some third sort, usually functions or relations. Three-sorted set theories are usually structural set theories. In common with other simply sorted set theory, the membership \in is a relation, in contrast to dependently sorted set theory, where membership is a typing judgment. In contrast to unsorted set theory and two-sorted set theory, sets and elements are different, and sets and elements are different from whatever relates sets and elements to each other (functions in categorical set theory, relations in allegorical set theory).

 Examples

 See also

Last revised on November 17, 2022 at 17:32:10. See the history of this page for a list of all contributions to it.