Patterns of resemblance: Difference between revisions
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The patterns of resemblance (PoR) are a system of ordinal-notations introduced by
A pattern is known as isominimal if it is pointwise least among all patterns isomorphic to it. The ''core'' is the set of ordinals which occur in an isominimal pattern.<ref>T. J. Carlson, "[https://www.sciencedirect.com/science/article/pii/S0168007200000403 Elementary Patterns of Resemblance]" (2001). Annals of Pure and Applied Logic vol. 108, pp.19--77.</ref> The definition of the core depends on which system is used, and as there are different systems going by the name "patterns of resemblance" (such as pure second-order patterns and additive first-order patterns), the term "the core" is context-dependent, and is defined analogously.<ref>https://arxiv.org/pdf/1710.01870.pdf</ref> For all systems analyzed, the core is a recursive ordinal.<ref>T. J. Carlson, "Elementary patterns of resemblance", corollary 6.12. Annals of Pure and Applied Logic vol. 108 (2001), pp.19--77.</ref><ref>T. J. Carlson, "Patterns of resemblance of order two", corollary 15.15. Annals of Pure and Applied Logic vol. 158 (2009), pp.90--124.</ref>
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