Arithmetical algorithms for elementary patterns

Archive for Mathematical Logic 54 (1-2):113-132 (2015)
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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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10.1007/s00153-014-0404-9

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Samuel Allen Alexander
Ohio State University (PhD)

Citations of this work

Pure Σ2-elementarity beyond the core.Gunnar Wilken - 2021 - Annals of Pure and Applied Logic 172 (9):103001.

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References found in this work

Ordinal arithmetic and $\Sigma_{1}$ -elementarity.Timothy J. Carlson - 1999 - Archive for Mathematical Logic 38 (7):449-460.
Elementary patterns of resemblance.Timothy J. Carlson - 2001 - Annals of Pure and Applied Logic 108 (1-3):19-77.
Patterns of resemblance of order 2.Timothy J. Carlson - 2009 - Annals of Pure and Applied Logic 158 (1-2):90-124.
Assignment of Ordinals to Patterns of Resemblance.Gunnar Wilken - 2007 - Journal of Symbolic Logic 72 (2):704 - 720.
The Bachmann-Howard Structure in Terms of Σ1-Elementarity.Gunnar Wilken - 2006 - Archive for Mathematical Logic 45 (7):807-829.

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