Definition of Urelements. Meaning of Urelements. Synonyms of Urelements

- urelements. As non-empty sets contain members while urelements do not, the unary relation is only needed to distinguish the empty set from urelements...
- Kripke–Platek set theory with urelements (KPU) is an axiom system for set theory with urelements, based on the traditional (urelement-free) Kripke–Platek set...
- Zermelo (1930). Urelements are objects that are not sets, but which can be elements of sets. In ZF set theory, there are no urelements, but in some other...
- theory, called ZU because it is equivalent to Zermelo set theory with urelements Zu (fish), a genus of ribbonfish Ziauddin University Zeppelin University...
- which are stronger than ZFC. The above systems can be modified to allow urelements, objects that can be members of sets but that are not themselves sets...
- Korea Polytechnic University, South Korea Kripke–Platek set theory with urelements, an axiom system for set theory Kwantlen Polytechnic University, a public...
- that the axiom of choice is false in NF (without urelements). In 1969, Jensen showed that adding urelements to NF yields a theory (NFU) that is provably consistent...
- proposed in 1908 the inclusion of urelements, from which he constructed a transfinite recursive hierarchy in 1930. Such urelements are used extensively in model...
- set theories. In set theories with urelements, one has to further make sure that the definition excludes urelements from appearing in ordinals. If α is...
- formulas with bounded quantifiers, as in Kripke–Platek set theory with urelements. The axiom schema of specification can almost be derived from the axiom...