  In this article the author claims that there is a paradigm shift from ZFC to
NFUM and further to NACT - due to philosophical reasons, not mathematical ones.
The goal is to construct systems where every "Not-Properclass" is a set! With
help of Non-Monotonic Logic, the consistent systems NACT-MoonW, NACT*W, and
NACT-SunW are producing "largest possible universes" of sets. Using
self-evident philosophical principles, three approximations are suggested:
NACT+NFUM-closed (to NACT*), NACT&ZFC4+(GCH) (also to NACT*) and NACT-NFUM (to
NACT-Sun). Also the system NACT[&ZFC4-closed]+(FCA) is considered.
  NFUM = NFU with (AC) and measurable properclass Ord. NFUM-closed is NFUM
where the set-constituting formulas Ai in the set operator need not only to be
stratified but also to be made parameter-free (i.e., have only x as free
variable over which the set is comprehended). In other formulas, free variables
are allowed. Keywords: Set Theory, ZFC, Naive Set Theory, Predicate-Extension,
Church Schema of Comprehension, NF, NFUM, Stratification, Universal Sets,
Eliminative Class Theory, NBG, NACT (= Naive Axiomatic Class Theory), NACT-Sun,
NACT-Moon, NACT-Star, NACT+NFUM-closed, ZFCK, NACT+NFUM, (GCH), (FCA) [= Finite
or Countable Anti-Thesis], NACT+ZFC4+(GCH), NACT[+ZFC4-[closed]+(FCA).
