urelement

Noun

urelement (plural urelements)

1. A mathematical object which is not a set but which can be an element of a set.
   • 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.1996, Scientific Books staff (translators), Yuri L. Ershov, Definability and Computability, Scientific Books, page viii
   • There may be no urelements; as we shall see, we can still build plenty of sets in this case. At stage 0 we can always build the empty set. If there are no urelements, this is the only set we can build. If there is one urelement, a, we can build the sets #92;empty and #92;#123;a#92;#125;. If there...2012, Nicholas J. J. Smith, Logic: The Laws of Truth, Princeton University Press, page 448

   Synonyms:

   atom