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Countable Version of Omega-Rule

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Logic, Language, Information and Computation (WoLLIC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6642))

Abstract

Omega-rule used by W. Buchholz to give an ordinal-free proof-theoretic analysis of \(\it \Pi^1_1\)-comprehension axiom has uncountable set of premises. We show how to make this set countable preserving the results and ideas of cut-elimination proof by Buchholz. The price is introduction of non-well founded derivation-like figures and use of continuous cut-elimination.

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References

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Author information

Authors and Affiliations

  1. Department of Philosophy, Stanford University, USA

    Grigori Mints

Authors
  1. Grigori Mints
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Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Gubkina 8, 117966, Moscow, Russia

    Lev D. Beklemishev

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

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Mints, G. (2011). Countable Version of Omega-Rule. In: Beklemishev, L.D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2011. Lecture Notes in Computer Science(), vol 6642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20920-8_21

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  • DOI: https://doi.org/10.1007/978-3-642-20920-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20919-2

  • Online ISBN: 978-3-642-20920-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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