Patterns of resemblance: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "The patterns of resemblance (PoR) are a system of ordinal-notations introduced by TJ Carlson. It is superficially similar to stability, yet is a notation for recursive rather than nonrecursive ordinals, and uses elementary substructures between ordinals themselves, instead of between ranks of the constructible universe. It uses a structure also found in BMS known as respecting forests, and was originally believed to have the same limit as BMS.") |
(Stability isn't an ordinal notation) |
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The patterns of resemblance (PoR) are a system of ordinal-notations introduced by TJ Carlson.
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Revision as of 21:56, 29 August 2023
The patterns of resemblance (PoR) are a system of ordinal-notations introduced by TJ Carlson. Like the notion of stability for ordinals it uses elementary substructures, however between ordinals themselves, instead of between ranks of the constructible universe. Carlson's \(<_n\)-relations have a property known as the respecting property, which also holds for the \(\Sigma_n\)-relations between ranks of \(L\), and for parenthood relations in BMS. For this reason, pure patterns of resemblance were originally believed to have the same limit of representable ordinals as BMS.