In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members...

ordinal notations (see ordinal analysis). However, it is not possible to decide effectively whether a given putative ordinal notation is a notation or...

ordinal notations. The proof-theoretic ordinal of such a theory T {\displaystyle T} is the supremum of the order types of all ordinal notations (necessarily...

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...

ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using recursive ordinal notations....

an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose...

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation...

ordinal notation, which is a concrete, effective description of the ordinal. An ordinal notation is an effective description of a countable ordinal by...

an ordinal notation in Kleene's O {\displaystyle {\mathcal {O}}} . Arithmetical hierarchy Large countable ordinal Ordinal analysis Ordinal notation Hartley...

no standard notation for ordinals beyond the Feferman–Schütte ordinal. There are several ways of representing the Feferman–Schütte ordinal, some of which...

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L...

Date and time notation in the United Kingdom records the date using the day–month–year format (31 December 1999, 31/12/99 or 31/12/1999). The time can...

neglected Z notation, a formal notation for specifying objects using Zermelo–Fraenkel set theory and first-order predicate logic Ordinal notation Set-builder...

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are...

infinite sets. For the ordinals he employed the Greek letter ω (omega). This notation is still in use today in ordinal notation of a finite sequence of...

regarded as ordinal notations. It contains ordinal notations for every computable ordinal, that is, ordinals below Church–Kleene ordinal, ω 1 CK {\displaystyle...

Veblen ordinal, a somewhat larger ordinal. There is no standard notation for ordinals beyond the Feferman–Schütte ordinal Γ0. Most systems of notation use...

are written as: I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII The notations IV and IX can be read as "one less than five" (4) and "one less than ten"...

Buchholz's ordinal is also the order type of the segment bounded by D 0 D ω 0 {\displaystyle D_{0}D_{\omega }0} in Buchholz's ordinal notation ( O T , <...

like "this is the third largest city in the country", which are called ordinal numbers. Natural numbers are also used as labels, like jersey numbers on...

functions from ordinals to ordinals), introduced by Oswald Veblen in Veblen (1908). If φ0 is any normal function, then for any non-zero ordinal α, φα is the...

Ackermann ordinal described by Ackermann (1951) is somewhat smaller than the small Veblen ordinal. There is no standard notation for ordinals beyond the...

countable ordinal such that to every limit ordinal α < μ there is assigned a fundamental sequence (a strictly increasing sequence of ordinals whose supremum...

the use of an ordinal marker or degree symbol: instead, various abbreviation of gradus (e.g., Gra., Gr., gr., G.). The modern notation appears in print...

ordinal < M {\displaystyle <M} ). Rathjen uses this to diagonalise over the weakly inaccessible hierarchy. It admits an associated ordinal notation T...

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...

is a countable ordinal much smaller than large countable ordinals. To express ordinals in the language of arithmetic, an ordinal notation is needed, i.e...

limit of this notation is the Takeuti–Feferman–Buchholz ordinal. Let P {\displaystyle P} be the class of additively principal ordinals. Buchholz showed...

{\displaystyle \uparrow } denotes Knuth's up-arrow notation.[citation needed] Ordinal arithmetic A. Rhea, "The Ordinals as a Consummate Abstraction of Number Systems"...

the convention of pronouncing the day and the month as an ordinal number, because ordinal numbers are written in German followed by a dot. German grammar...