mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though...

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...

mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by...

give systems of ordinal notations for ordinals less than the small and large Veblen ordinals. Ackermann (1951) described a system of ordinal notation rather...

mathematics, the Veblen ordinal is either of two large countable ordinals: The small Veblen ordinal The large Veblen ordinal Veblen function This disambiguation...

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

ordinal can be defined as the smallest ordinal that cannot be obtained by starting with 0 and using the operations of ordinal addition and the Veblen...

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

the ordinals that cannot be obtained from smaller ordinals using addition and the Veblen functions. It is, of course, possible to describe ordinals beyond...

\vartheta } ordinal collapsing function. (The small Veblen ordinal equals ϑ ( Ω ω ) {\displaystyle \vartheta (\Omega ^{\omega })} in this ordinal notation...

The Bachmann–Howard ordinal is ψ(εΩ+1). The Bachmann–Howard ordinal can also be defined as φεΩ+1(0) for an extension of the Veblen functions φα to certain...

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

by the small Veblen ordinal. Jäger's ψ is a hierarchy of single-argument ordinal functions ψκ indexed by uncountable regular cardinals κ smaller than the...

mathematics, ψ0(Ωω), widely known as Buchholz's ordinal[citation needed], is a large countable ordinal that is used to measure the proof-theoretic strength...

Oriente, former Mexican charter airline (ICAO code: SVO) Small Veblen ordinal, a large countable ordinal Social value orientations, a psychological construct...

no. 1 (2002) F. Ranzi, T. Strahm, "A flexible type system for the small Veblen ordinal" (2019). Archive for Mathematical Logic 58: 711–751. K. Fujimoto...

1-CA0. Ordinal analysis confirms the strength of Kruskal's theorem, with the proof-theoretic ordinal of the theorem equaling the small Veblen ordinal (sometimes...

functions of ordinals and used an extension of them to define the small and large Veblen ordinals. In World War II he was involved in overseeing ballistics work...

the "limit" obtained by transfinite recursion from a sequence of smaller limit ordinals: ε 0 = ω ω ω ⋅ ⋅ ⋅ = sup { ω , ω ω , ω ω ω , ω ω ω ω , … } , {\displaystyle...

theory and proof theory, the Takeuti–Feferman–Buchholz ordinal (TFBO) is a large countable ordinal, which acts as the limit of the range of Buchholz's psi...

exponentiation, including ordinal versions of tetration, pentation, and hexation. See also Veblen function. Every ordinal number α can be uniquely written...

origin of the Church–Kleene ordinal in the definition of the lightface hierarchy. Projective hierarchy Wadge hierarchy Veblen hierarchy P. G. Hinman, *Recursion-Theoretic...

\Omega )})} . The proof-theoretic ordinal of ID1 (the Bachmann-Howard ordinal) is also the proof-theoretic ordinal of K P {\displaystyle {\mathsf {KP}}}...

ISBN 978-3-030-49423-0. The Veblen approach was quite sufficient even for the ordinal, now known as the Feferman–Schütte ordinal, Γ0 for predictive analysis...

^{\omega }})} is the small Veblen ordinal, ψ 0 ( Ω Ω Ω ) {\displaystyle \psi _{0}(\Omega ^{\Omega ^{\Omega }})} is the large Veblen ordinal, ψ 0 ( Ω ↑↑ ω )...

ISBN 978-3-030-49423-0. The Veblen approach was quite sufficient even for the ordinal, now known as the Feferman–Schütte ordinal, Γ0 for predictive analysis...

hierarchy φ A Veblen function ω 1.  The smallest infinite ordinal 2.  ωα is an alternative name for ℵα, used when it is considered as an ordinal number rather...

proof theoretic ordinal φ ( ε 0 , 0 ) {\displaystyle \varphi (\varepsilon _{0},0)} , which is the first common fixed point of the Veblen functions φ β {\displaystyle...

different notions of social welfare used by economists: Ordinal (or ranked voting) functions only use ordinal information, i.e. whether one choice is better than...

players have incomplete information regarding the types of other players. Ordinal Pareto efficiency is an adaptation of Pareto efficiency to settings in...