First Order Theories for Nonmonotone Inductive Definitions: Recursively Inaccessible and Mahlo

Journal of Symbolic Logic 66 (3):1073-1089 (2001)
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Abstract

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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Citations of this work

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.
Theories of Frege structure equivalent to Feferman's system T 0.Daichi Hayashi - 2025 - Annals of Pure and Applied Logic 176 (1):103510.

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References found in this work

Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
A well-ordering proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
Proof theory and ordinal analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.

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