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wellordered's Usage Examples:

If the axiom of choice (AC) holds (or even if the reals can be wellordered), then Θ is simply ( 2 ℵ 0 ) + {\displaystyle (2^{\aleph _{0}})^{+}}.

articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering.

choice, the existence of a scale on a pointset is trivial, as A can be wellordered and each φn can simply enumerate A.

starting with the open subsets of X {\displaystyle X} , and transfinitely iterating the operations of complementation and wellordered union.

axiom of ZFC set theory which in one form states that every set can be wellordered.

obtained by starting with the open subsets of X {\displaystyle X} , and transfinitely iterating the operations of complementation and wellordered union.

Note that the set of ∞-Borel sets may not actually be closed under wellordered union; see below.

operations of complementation and wellordered union.

what is also known as Hartogs"s theorem: for every set x there is a wellordered set that cannot be injectively embedded in x.