-
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...
-
extension set
theory Kripke–Platek set
theory Kripke–Platek set
theory with
urelements Scott–Potter set
theory Constructive set
theory Zermelo set
theory General...
-
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...
-
proposed in 1908 the
inclusion of
urelements, from
which he
constructed a
transfinite recursive hierarchy in 1930. Such
urelements are used
extensively in model...
-
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...
- {\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 ⊆...
-
formulas with
bounded quantifiers, as in Kripke–Platek set
theory with
urelements. The
axiom schema of
specification is
implied by the
axiom schema of replacement...
