For instance, it has a projective well ordering of the reals, and it satisfies the GCH.
The as-prepared NCA powders display well ordering of hexagonal two-dimensional layer structure with low degree of cation mixing under appropriate conditions: IR heating time (5 h) and rheological-phase method.
It asserts the equivalence of ∃yϕ y) with ¬∀y¬ϕ y), using classical logic, but there is no way one can construct such an x, for example, when ϕ(x) asserts the existence of a well-ordering of the reals, as was proved by Feferman.
The second formulation of CH asserts that every well-ordering of the reals has order type less than ℵ2.
Gödel defines a book-keeping device, a well-ordering of all tuples of variables arising from a need to satisfy φ as dictated by (Q).
Contrary to König, Richard did not rely upon the well-ordering of the continuum, and the proposed solution is interesting for the foundational debate to come.
This ordinal path stretches as far into the transfinite as the predicative ordinals reach, where an ordinal is predicative if it measures the length of a provable well-ordering of the natural numbers.
But there again it is often natural to consider the EXT quantifier W rel, where (W rel)M A, R) says that R is a well-ordering of A. 23.
In the second version, at each stage one actually shows not only that each well-ordering of reals in the definability class has ordertype less than ℵ2, but also that it has ordertype less than ℵ1.
One way this could be is if there is no well-ordering of worlds: some worlds are sufficiently different in kind that they are incommensurate with each other (neither is better than the other, nor are they equal).
