Abstract
Elementary patterns of resemblance notate ordinals up to the ordinal of \({\Pi^1_1 - CA_0}\). We provide ordinal multiplication and exponentiation algorithms using these notations.
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Alexander, S.: The patterns of resemblance ordinal calculator. http://www.xamuel.com/patterns/ (2012)
Bès A.: Decidability and definability results related to the elementary theory of ordinal multiplication. Fundamenta Mathematicae 171, 197–211 (2002)
Carlson T.J.: Ordinal arithmetic and Σ1 elementarity. Arch. Math. Logic 38, 449–460 (1999)
Carlson T.J.: Knowledge, machines, and the consistency of Reinhardt’s strong mechanistic thesis. Ann. Pure Appl. Logic 105, 51–82 (2000)
Carlson T.J.: Elementary patterns of resemblance. Ann. Pure Appl. Logic 108(1), 19–77 (2001)
Carlson T.J.: Patterns of resemblance of order 2. Ann. Pure Appl. Logic 158(1–2), 90–124 (2009)
Carlson T.J., Wilken G.: Normal forms for elementary patterns. J. Symb. Logic 77(1), 174–194 (2012)
Wilken, G.: Σ1-elementarity and Skolem hull operators. Thesis (dissertation), University of Münster (2004)
Wilken G.: The Bachmann–Howard structure in terms of Σ1-elementarity. Arch. Math. Logic 45(7), 807–829 (2006)
Wilken G.: Assignment of ordinals to elementary patterns of resemblance. J. Symb. Logic 72(2), 704–720 (2007)
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Alexander, S.A. Arithmetical algorithms for elementary patterns. Arch. Math. Logic 54, 113–132 (2015). https://doi.org/10.1007/s00153-014-0404-9
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DOI: https://doi.org/10.1007/s00153-014-0404-9