Noun
powerset (plural powersets)
Alternative spelling of power set
An ultrafilter on ℘(ω) is Ramsey if and only if it is minimal in the Rudin–Keisler ordering of non-principal powerset ultrafilters. Source: Internet
For ultrafilters on a powerset ℘(S), a principal ultrafilter consists of all subsets of S that contain a given element s of S. Each ultrafilter on ℘(S) that is also a principal filter is of this form. Source: Internet
Given a set S, a partial ordering ⊆ can be defined on the powerset P(S) by subset inclusion, turning (P(S),⊆) into a lattice. Source: Internet
In summary, one can say that every complete lattice is isomorphic to the image of a closure operator on a powerset lattice. Source: Internet
So some of the power of comprehension was added back via the other existence axioms of ZF set theory (pairing, union, powerset, replacement, and infinity) which may be regarded as special cases of comprehension. Source: Internet
Such a least cut does indeed exist and one has a closure operator on the powerset lattice of all elements. Source: Internet