First order theories for nonmonotone inductive definitions: Recursively inaccessible and mahlo

Journal of Symbolic Logic 66 (3):1073-1089 (2001)
In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms a la Richter with recursively inaccessible and Mahlo closure ordinals is given
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DOI 10.2307/2695093
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Reflections on Reflections in Explicit Mathematics.Gerhard Jäger & Thomas Strahm - 2005 - Annals of Pure and Applied Logic 136 (1-2):116-133.
A Note on Theories for Quasi-Inductive Definitions.Riccardo Bruni - 2009 - Review of Symbolic Logic 2 (4):684-699.

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