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Logica Universalis

, Volume 5, Issue 1, pp 1–19 | Cite as

A Buchholz Rule for Modal Fixed Point Logics

  • Gerhard Jäger
  • Thomas StuderEmail author
Article

Abstract

Buchholz’s Ωμ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz (Iterated inductive definitions and subsystems of analysis: recent proof theoretic studies. Lecture notes in mathematics, vol. 897, pp. 189–233, Springer, Berlin, 1981).

Mathematics Subject Classification (2010)

03B45 03B70 03F03 03F05 

Keywords

Modal μ-calculus proof theory Buchholz rule 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institut für Informatik und angewandte MathematikUniversität BernBernSwitzerland

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