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About: Large countable ordinal     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:OrdinalNumber113597280, within Data Space : dbpedia.org associated with source document(s)

Type: Thingyago:WikicatOrdinalNumbersyago:Abstraction100002137yago:DefiniteQuantity113576101yago:Measure100033615yago:Number113582013yago:OrdinalNumber113597280 New Facet based on Instances of this Class

In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of relevance to proof theory still have computable ordinal notations (see ordinal analysis). However, it is not possible to decide effectively whether a given putative ordinal notation is a notation or not (for reasons somewhat analogous to the unsolvability of the halting problem); various more-concrete ways of defining ordinals that definitely have notations are available.