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| In mathematics, the '''small Veblen ordinal''' is a certain [[large countable ordinal]], named after [[Oswald Veblen]]. It is occasionally called the '''Ackermann ordinal''', though the [[Ackermann ordinal]] described by {{harvtxt|Ackermann|1951}} is somewhat smaller than the small Veblen ordinal.
| | My name is Derick and I am studying English Literature and Integrated International Studies at Fresnes / France.<br><br>Here is my web page; [http://iz.sa/wordpressbackup197513 backup plugin] |
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| Unfortunately there is no standard notation for ordinals beyond the [[Feferman–Schütte ordinal]] Γ<sub>0</sub>. Most systems of notation use symbols such as ψ(α), θ(α), ψ<sub>α</sub>(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".
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| The '''small Veblen ordinal''' <math>\phi_{{\Omega^\omega}}(0)</math> or <math>\theta(\Omega^\omega)</math> or <math>\psi(\Omega^{\Omega^\omega})</math> is the limit of ordinals that can be described using a version of [[Veblen function]]s with finitely many arguments. It is the ordinal that measures the strength of [[Kruskal's theorem]]. It is also the ordinal type of a certain ordering of [[rooted tree]]s {{harv|Jervell|2005}}.
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| ==References==
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| *{{citation|mr=0039669 |last=Ackermann|first= Wilhelm |title=Konstruktiver Aufbau eines Abschnitts der zweiten Cantorschen Zahlenklasse
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| |journal=Math. Z. |volume=53|year=1951|pages= 403–413|doi=10.1007/BF01175640|issue=5}}
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| *{{citation |url=http://folk.uio.no/herman/finord.pdf |first=Herman Ruge |last=Jervell |series=Lecture Notes in Computer Science
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| |publisher =Springer |place=Berlin / Heidelberg |volume =3526 |title=New Computational Paradigms |year=2005 |isbn =978-3-540-26179-7
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| |doi =10.1007/11494645_26 |pages =211–220 |chapter=Finite Trees as Ordinals}}
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| *{{citation|mr=1212407 |last=Rathjen|first= Michael|last2= Weiermann|first2= Andreas |title=Proof-theoretic investigations on Kruskal's theorem |journal=Ann. Pure Appl. Logic|volume= 60 |year=1993|issue= 1|pages= 49–88 |url=http://www.amsta.leeds.ac.uk/Pure/staff/rathjen/kruskal.ps |doi=10.1016/0168-0072(93)90192-G}}
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| *{{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 |jstor=1988605|doi= 10.2307/1988605}}
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| *{{cite arxiv |last=Weaver|first=Nik|eprint=math/0509244|title=Predicativity beyond Gamma_0|year=2005 |class=math.LO}}
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| {{countable ordinals}}
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| [[Category:Ordinal numbers]]
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My name is Derick and I am studying English Literature and Integrated International Studies at Fresnes / France.
Here is my web page; backup plugin