Proof theory of weak compactness

Journal of Mathematical Logic 13 (1):1350003 (2013)
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Abstract

We show that the existence of a weakly compact cardinal over the Zermelo–Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and Mahlo operations.

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10.1142/s0219061313500037

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Citations of this work

Intuitionistic fixed point theories over set theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.
Conservations of first-order reflections.Toshiyasu Arai - 2014 - Journal of Symbolic Logic 79 (3):814-825.
Cut-elimination for ω1.Toshiyasu Arai - 2018 - Annals of Pure and Applied Logic 169 (12):1246-1269.

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References found in this work

Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.

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