- Ackermann ordinal
In mathematics, the Ackermann ordinal is a certain
large countable ordinal , named afterWilhelm Ackermann . The term "Ackermann ordinal" is also occasionally used for thesmall Veblen ordinal , a somewhat larger ordinal.Unfortunately there is no standard notation for ordinals beyond the Feferman–Schütte ordinal Γ0. Most systems of notation use symbols such as ψ(α), θ(α), ψα(β), some of which are modifications of the
Veblen function s to produce countable ordinals even for uncountable arguments, and some of which are "collapsing function s".The smaller Ackermann ordinal is the limit of a system of ordinal notations invented by harvtxt|Ackermann|1951, and is sometimes denoted by phi_Omega^2(0) or heta(Omega^2) or psi(Omega^2). Ackermann's system of notation is weaker than the system introduced much earlier by harvtxt|Veblen|1908, which he seems to have been unaware of.
References
*citation|id=MR|0039669
last=Ackermann|first= Wilhelm
title=Konstruktiver Aufbau eines Abschnitts der zweiten Cantorschen Zahlenklasse
journal=Math. Z. |volume=53|year=1951|pages= 403-413|doi= 10.1007/BF01175640
*citation|title= Continuous Increasing Functions of Finite and Transfinite Ordinals
first= Oswald |last=Veblen
journal= Transactions of the American Mathematical Society|volume= 9|issue= 3|year= 1908|pages=280-292
url= http://links.jstor.org/sici?sici=0002-9947%28190807%299%3A3%3C280%3ACIFOFA%3E2.0.CO%3B2-1
*citation|last=Weaver|first=Nik|url=http://arxiv.org/abs/math/0509244|title=Predicativity beyond Gamma_0|year=2005
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