and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering. Every non-empty...

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict...

axiom of ZFC set theory which in one form states that every set can be wellordered. In ZF set theory, i.e. ZFC without the axiom of choice, the following...

such a cardinal would have additional consequences. If the reals can be wellordered, then Θ {\displaystyle \Theta } is simply ( 2 ℵ 0 ) + {\displaystyle...

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

arithmetic" (2017) F. Ranzi, From a Flexible Type System to Metapredicative Wellordering Proofs. Doctoral thesis, University of Bern, 2015. A. Cantini, "On the...

S2CID 15020752. Dybjer, Peter (1997). "Representing inductively defined sets by wellorderings in Martin-Löf's type theory". Theoretical Computer Science. 176 (1–2):...

{\displaystyle \leq } induces a wellordering on the quotient X / ∼ . {\displaystyle X/{\sim }.} The order-type of this induced wellordering is an ordinal, referred...

ingredient of the construction is the comparison lemma that allows giving a wellordering of the relevant mice. At the level of strong cardinals and above, one...

doi:10.1016/0022-4049(95)00147-6, MR 1382244 Burckel, Serge (1997), "The wellordering on positive braids", Journal of Pure and Applied Algebra, 120 (1): 1–17...