nLab urelement

Redirected from "urelements".
Idea

Context

Foundations

foundations

The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms

Idea

An urelement, also called an atom, in a material set theory is a thing which is not a set. Many common material set theories, such as ZFC, do not by default allow urelements; thus everything is a set and all sets are pure. However, they can usually be easily modified to allow urelements — one such version is ZFA. Quine's New Foundations is consistent with the axiom of choice only if it allows urelements.

Last revised on October 18, 2020 at 19:11:20. See the history of this page for a list of all contributions to it.