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Pell Equations and Weak Regularity Principles

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Logic and Theory of Algorithms (CiE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

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Abstract

We study the strength of weak forms of the Regularity Principle in the presence of IE 1 (induction on bounded existential formulas) relative to other subsystems of PA. In particular, the Bounded Weak Regularity Principle is formulated, and it is shown that when applied to E 1 formulas, this principle is equivalent over \(IE_1^-\) to IΔ 0 + exp.

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Authors and Affiliations

  1. Department of Mathematics, University of Aegean, GR-832 00, Karlovassi, Greece

    Charalampos Cornaros

Authors
  1. Charalampos Cornaros
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Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

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© 2008 Springer-Verlag Berlin Heidelberg

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Cornaros, C. (2008). Pell Equations and Weak Regularity Principles. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-69407-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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