Systems of set theory

one of several theories of sets used in the discussion of the foundations of mathematics; defined informally, in natural language

variant of ZFC, the standard axiomatic set theory

sets whose elements have degrees of membership

axiomatic set theory

in set theory, a set which contains all objects, including itself

system of set theory (in mathematics)

axiomatic set theory permitting set comprehension by stratified formulae, hence with a universal set, but in which the singleton map 𝑥↦{𝑥} fails to exist

alternative to the standard Zermelo–Fraenkel set theory with the axiom of choice

formal approximation of a crisp (i.e. conventional) set

first‐order axiomatic set theory permitting proper classes and class comprehension with bound (possibly proper) classes

variants of axiomatic set theory that allow sets to be elements of themselves