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...
- due to Zermelo. 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...
- 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...
- 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...
- early as 1922 that the axiom of choice may fail in a variant of ZF with urelements, through the technique of permutation models introduced by Abraham Fraenkel...
- consistency of NF. NF with urelements (NFU) is an important variant of NF due to Jensen and clarified by Holmes. Urelements are objects that are not sets...
- proposed in 1908 the inclusion of urelements, from which he constructed a transfinite recursive hierarchy in 1930. Such urelements are used extensively in model...
- {\displaystyle Z=\{X,Y\}} .) A set X {\displaystyle X} that does not contain urelements is transitive if and only if it is a subset of its own power set, X ⊆...
- 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...
- extension set theory Kripke–Platek set theory Kripke–Platek set theory with urelements Scott–Potter set theory Constructive set theory Zermelo set theory General...