Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π₂⁰-operators

Journal of Symbolic Logic 69 (3):830-850 (2004)

In this paper, we prove the wellfoundedness of recursive notation systems for reflecting ordinals up to Π₃-reflection by relevant inductive definitions
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DOI 10.2178/jsl/1096901770
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References found in this work BETA

Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Ordinal Diagrams for Recursively Mahlo Universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.
Laforte, G., See Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95:287.

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Citations of this work BETA

Proof Theory of Weak Compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
Proof Theory for Theories of Ordinals II:< I> Π_< Sub> 3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
Epsilon Substitution Method for [Π0 1, Π0 1]-FIX.T. Arai - 2005 - Archive for Mathematical Logic 44 (8):1009-1043.
A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.

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