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uncountable ordinal

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  • Ordinal collapsing function — In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger …   Wikipedia

  • Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …   Wikipedia

  • Uncountable set — Uncountable redirects here. For the linguistic concept, see Uncountable noun. In mathematics, an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal… …   Wikipedia

  • Ordinal notation — In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language. There are many such schemes of ordinal… …   Wikipedia

  • Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… …   Wikipedia

  • Bachmann–Howard ordinal — In mathematics, the Bachmann–Howard ordinal (or Howard ordinal) is a large countable ordinal.It is the proof theoretic ordinal of several mathematical theories, such as Kripke–Platek set theory (with the axiom of infinity) and the system CZF of… …   Wikipedia

  • Limit ordinal — A limit ordinal is an ordinal number which is neither zero nor a successor ordinal. Various equivalent ways to express this are: *It cannot be reached via the ordinal successor operation S ; in precise terms, we say lambda; is a limit ordinal if… …   Wikipedia

  • Small Veblen ordinal — In mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though the Ackermann ordinal described by harvtxt|Ackermann|1951 is somewhat smaller than… …   Wikipedia

  • Ackermann ordinal — In mathematics, the Ackermann ordinal is a certain large countable ordinal, named after Wilhelm Ackermann. The term Ackermann ordinal is also occasionally used for the small Veblen ordinal, a somewhat larger ordinal. Unfortunately there is no… …   Wikipedia

  • Large Veblen ordinal — In mathematics, the large Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. There is no standard notation for ordinals beyond the Feferman–Schütte ordinal Γ0. Most systems of notation use symbols such as psi;(α),… …   Wikipedia

  • Ε₀ — In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map. Consequently, they are not reachable from 0 via a series of applications of the chosen… …   Wikipedia

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