A Buchholz Rule for Modal Fixed Point Logics |
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Authors: | Gerhard Jäger Thomas Studer |
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Affiliation: | (1) Vienna University of Technology, Wiedner Hauptstra?e 8-10, 1040 Vienna, Austria;(2) Vienna University of Technology, Favoritenstra?e 9, 1040 Vienna, Austria |
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Abstract: | Buchholz’s Ω μ+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). |
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