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 15:11:20.
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