urelement

== English == === Alternative forms === ur-element === Etymology === From ur- (“primordial”) +‎ element. === Noun === urelement (plural urelements) (set theory) A mathematical object which is not a set but which can be an element of a set. Synonym: atom 1996, Scientific Books staff (translators), Yuri L. Ershov, Definability and Computability, Scientific Books, page viii, The introduction of urelements would seem to be a technical improvement; however, now we know that just such an extension of the notion of the admissible set led to the universal theory of computability based on the notion of definability by formulas with (in a broad sense) effective semantics. ==== Usage notes ==== The standard axiomatisation of set theory, ZFC, ignores urelements. (By the axiom of extensionality, two sets whose only difference is that one contains urelements which the other does not would be equal.) ==== Derived terms ==== KPU NFU ==== Translations ==== === See also === hereditary set pure set Quine atom === Further reading === Urelement on Wikipedia.Wikipedia Axiom of extensionality on Wikipedia.Wikipedia Hereditary set on Wikipedia.Wikipedia Kripke–Platek set theory with urelements on Wikipedia.Wikipedia New Foundations on Wikipedia.Wikipedia urelement on nLab Urelement on Wolfram MathWorld