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

In mathematics, the Feferman–Schütte ordinal (Γ0) is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such...

uncountable ordinals. There are several ways to do this, described to some extent in the article on ordinal collapsing function. The Bachmann–Howard ordinal (sometimes...

Psi function can refer, in mathematics, to the ordinal collapsing function ψ ( α ) {\displaystyle \psi (\alpha )} the Dedekind psi function ψ ( n ) {\displaystyle...

}+1}}(0)} in Feferman's theta function, an ordinal collapsing function invented by Solomon Feferman. It is the proof-theoretic ordinal of several formal theories:...

Optimum Coding in the Frequency Domain Ordinal collapsing function, a process used for reaching large ordinals in the field of set theory Ordnance Clothing...

Howard (1972). The Bachmann–Howard ordinal is defined using an ordinal collapsing function: εα enumerates the epsilon numbers, the ordinals ε such that ωε = ε. Ω =...

Rathjen's  ψ {\displaystyle \psi } psi function is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo cardinals M {\displaystyle...

mathematical game on a labeled tree Buchholz psi functions, a system of ordinal collapsing functions Buchholz's ID hierarchy, a hierarchy of inductively...

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

of banks in economic models The ordinal collapsing function developed by Solomon Feferman The Heaviside step function In pharmacology, the fraction of...

ordinal collapsing functions as defined in their respective citations. Ψ represents either Rathjen's or Stegert's Psi. φ represents Veblen's function...

produce countable ordinals even for uncountable arguments, and some of which are ordinal collapsing functions. The large Veblen ordinal is sometimes denoted...

adjustment to a U-value, accounting for thermal bridge effects. The ordinal collapsing function and notation developed by Wilfried Buchholz. In Biblical studies...

modifications of the Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions". The last one is...

observatory) in Zürich. He introduced the Bachmann–Howard ordinal and ordinal collapsing functions. "Zum Hinschied von Dr. Heinz Bachmann (1924 bis 2022)"...

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

predicative mathematics. In particular, he introduced the Feferman–Schütte ordinal as a measure of the strength of certain predicative systems. Feferman was...

Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions". The small Veblen ordinal θ Ω...

enumerated by φ2 (see ordinal collapsing function.) Continuing in this vein, one can define maps φα for progressively larger ordinals α (including, by this...

Buchholz's psi-functions are a hierarchy of single-argument ordinal functions ψ ν ( α ) {\displaystyle \psi _{\nu }(\alpha )} introduced by German mathematician...

\mathrm {Ord} \subset L\subseteq V} , properties of ordinals that depend on the absence of a function or other structure (i.e. Π 1 Z F {\displaystyle \Pi...

own ordinals, cardinals, real numbers, and so on. This results in a lot of bookkeeping to relate the various types with each other. In ZFC functions are...

surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there...

the same functions recursive. Specifically, its proof-theoretic large countable ordinal is the Bachmann–Howard ordinal. This is also the ordinal of classical...

finite sequences of ordinals less than a given cardinal λ. If λ is uncountable then forcing with this poset collapses λ to ω. Collapsing a cardinal to another:...

constructible universe L {\displaystyle L} satisfies "for every countable ordinal α {\displaystyle \alpha } , there is an α {\displaystyle \alpha } -Erdős...

other two, are mapped to the same ordinal, then the three nodes are comparable. This can be done without collapsing ℵ1, and results in a tree with exactly...

ordinal β 1.  βX is the Stone–Čech compactification of X 2.  An ordinal γ A gamma number, an ordinal of the form ωα Γ The Gamma function of ordinals....

categories are ordered, one can use the ordinal logistic regression (for example the proportional odds ordinal logistic model). See § Extensions for further...