A Survey on Ordinal Notations Around the Bachmann–Howard Ordinal

  • Wilfried Buchholz
Part of the Outstanding Contributions to Logic book series (OCTR, volume 13)


Various ordinal functions which in the past have been used to describe ordinals not much larger than the Bachmann–Howard ordinal are set into relation. Special efforts are made to reveal the intrinsic connections between Feferman’s \(\theta \)-functions and the Bachmann hierarchy.


Bachmann–Howard ordinal Bachmann hierarchy Fundamental sequence Klammersymbol Normal function 

2010 Mathematics Subject Classification



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Authors and Affiliations

  1. 1.Mathematisches Institut der Universität MünchenMünchenGermany

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