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).
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Jäger, G., Studer, T. A Buchholz Rule for Modal Fixed Point Logics. Log. Univers. 5, 1–19 (2011). https://doi.org/10.1007/s11787-010-0022-1
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DOI: https://doi.org/10.1007/s11787-010-0022-1