Abstract.
The standard method of generating countable ordinals from uncountable ordinals can be replaced by a use of fixed point extractors available in the term calculus of Howard’s system. This gives a notion of the intrinsic complexity of an ordinal analogous to the intrinsic complexity of a function described in Gödel’s T.
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Simmons, H. A comparison of two systems of ordinal notations. Arch. Math. Logic 43, 65–83 (2004). https://doi.org/10.1007/s00153-003-0177-z
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DOI: https://doi.org/10.1007/s00153-003-0177-z