alternative set theory
alternative to the standard Zermelo–Fraenkel set theory
New Foundations
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
constructive set theory
axiomatic set theories based on the principles of mathematical constructivism
non-well-founded set theory
variants of axiomatic set theory that allow sets to be elements of themselves
positive set theory
class of alternative set theories
S
system of mathematical set theory
Pocket set theory
an alternative set theory in which there are only two infinite cardinal numbers
Ackermann set theory
axiomatic set theory proposed by Wilhelm Ackermann