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Infinity-Borel set — In set theory, a subset of a Polish space X is infin; Borel if itcan be obtained by starting with the open subsets of X, and transfinitely iterating the operations of complementation and wellordered union (but see the caveat below). Formal… … Wikipedia
Hartogs number — In mathematics, specifically in axiomatic set theory, a Hartogs number is a particular kind of cardinal number. It was shown by Friedrich Hartogs in 1915, from ZF alone (that is, without using the axiom of choice), that there is a least… … Wikipedia
Θ (set theory) — In set theory, Theta; is the least ordinal α such that there is no surjection from the reals onto α.If the axiom of choice (AC) holds (or even if the reals can be wellordered) then Theta; is simply (2^{aleph 0})^+, the cardinal successor of the… … Wikipedia
Well-order — In mathematics, a well order relation (or well ordering) on a set S is a total order on S with the property that every non empty subset of S has a least element in this ordering.Equivalently, a well ordering is a well founded total order.The set… … Wikipedia

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