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

Buchholz (surname) Buchholz hydra, a mathematical game on a labeled tree Buchholz psi functions, a system of ordinal collapsing functions Buchholz's ID...

Psi /ˈ(p)saɪ, ˈ(p)siː/ (P)SY, (P)SEE (uppercase Ψ, lowercase ψ or 𝛙; Greek: ψι psi [ˈpsi]) is the twenty-third and penultimate letter of the Greek alphabet...

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

of infinity (KP). Buchholz's ψ {\displaystyle \psi }  is a hierarchy of single-argument functions ψ ν : O n → O n {\displaystyle \psi _{\nu }:{\mathsf...

ordinal, Γ0, up to at least the Bachmann–Howard ordinal. Using Buchholz psi functions one can extend this definition easily to the ordinal of transfinitely...

In 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...

{\displaystyle \psi _{\alpha }} , where α {\displaystyle \alpha } is the label of the node, and ψ {\displaystyle \psi } is Buchholz's function. The resulting...

1 ) {\displaystyle \psi _{0}(\varepsilon _{\Omega _{\omega }+1})} . It is the supremum of the range of Buchholz's psi functions. It was first named by...

_{v}+1}0=\psi _{0}(\varepsilon _{\Omega _{v}+1})} for v ≤ ω. Yet, while this system is powerful, it does not qualify as an ordinal notation. Buchholz did create...

"Rapidly Growing Ramsey Functions". Annals of Mathematics. 113 (2): 267–314. doi:10.2307/2006985. ISSN 0003-486X. JSTOR 2006985. Buchholz, Wilfried (1984-11-27)...

{\psi }}M\psi +{\bar {\eta }}\psi +{\bar {\psi }}\eta }\,D{\bar {\psi }}\,D\psi =\int e^{\left({\bar {\psi }}+{\bar {\eta }}M^{-1}\right)M\left(\psi +M^{-1}\eta...

In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral...

ψ ( ε Ω + 1 ) {\displaystyle \psi (\varepsilon _{\Omega +1})} in Madore's ψ. 4.^ Uses Madore's ψ rather than Buchholz's ψ. 5.^ Can also be commonly written...

_{1}\psi _{2}+\psi _{1}\psi _{2}\psi _{1})+{\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{2}\psi _{1}+\psi _{2}\psi _{1}\psi _{1}+\psi _{2}\psi _{1}\psi _{1})\right)\\=&{\frac...

2 ‖ Φ ‖ 2 {\displaystyle P{\big (}[\Psi ],[\Phi ]{\big )}={\frac {|\langle \Psi ,\Phi \rangle |^{2}}{\lVert \Psi \rVert ^{2}\lVert \Phi \rVert ^{2}}}}...

to the equations, universally denoted as ψ or Ψ (Greek psi), are referred to as "wave functions" in the context of RQM, and "fields" in the context of...

| ψ ⟩ {\displaystyle |\psi \rangle } is no longer a spatial wave function in the traditional sense of a complex-valued function that is defined on a 3-dimensional...

\end{aligned}}} Since interacting correlation functions can be expressed in terms of free correlation functions, only the latter need to be evaluated in order...

on functions f in classical phase space, then the following properties are usually considered desirable: Q x ψ = x ψ {\displaystyle Q_{x}\psi =x\psi }...

gauge functions which satisfy the wave equation ∂ 2 ψ ∂ t 2 = c 2 ∇ 2 ψ {\displaystyle {\frac {\partial ^{2}\psi }{\partial t^{2}}}=c^{2}\nabla ^{2}\psi }...

condensates must be of the form ⟨ ψ ¯ ψ ⟩ {\displaystyle \langle {\overline {\psi }}\psi \rangle } , where ψ is the fermion field. Similarly a tensor field, Gμν...

_{l}}\langle 0|\mathrm {T} [\Psi _{\beta _{1}}(y_{1})...\Psi _{\beta _{n'}}(y_{n'}){\bar {\Psi }}_{\alpha _{1}}(x_{1})...{\bar {\Psi }}_{\alpha _{n}}(x_{n})]|0\rangle...

Feferman–Schütte ordinal, some of which use ordinal collapsing functions: ψ ( Ω Ω ) {\displaystyle \psi (\Omega ^{\Omega })} , θ ( Ω ) {\displaystyle \theta (\Omega...

R ψ L ) {\displaystyle -m{\bar {\psi }}\psi =-m({\bar {\psi }}_{\rm {L}}\psi _{\rm {R}}+{\bar {\psi }}_{\rm {R}}\psi _{\rm {L}})} i.e. contribution from...

{\displaystyle \psi (\Omega ^{\Omega ^{\omega }})} is the limit of ordinals that can be described using a version of Veblen functions with finitely many...

0 ) = x x ( t ) = y e i S D x , {\displaystyle \psi _{t}(y)=\int \psi _{0}(x)K(x-y;t)\,dx=\int \psi _{0}(x)\int _{x(0)=x}^{x(t)=y}e^{iS}\,{\mathcal {D}}x...

{\displaystyle {\mathcal {S}}=\int {\bar {\psi }}\left(i\hbar c\,\gamma ^{\mu }\partial _{\mu }-mc^{2}\right)\psi \,\mathrm {d} ^{4}x} The global symmetry...

}F^{\mu \nu }+i{\bar {\psi }}\gamma ^{\mu }\partial _{\mu }\psi -e{\bar {\psi }}\gamma ^{\mu }A_{\mu }\psi -m{\bar {\psi }}\psi } = − 1 4 F μ ν F μ ν +...

\psi ={\begin{pmatrix}\psi _{1}\\\psi _{2}\\\psi _{3}\end{pmatrix}},{\overline {\psi }}={\begin{pmatrix}{\overline {\psi }}_{1}^{*}\\{\overline {\psi...