# A Sneak Preview of Proof Theory of Ordinals( Infinity in Philosophy and Mathematics)

@article{Arai2011ASP, title={A Sneak Preview of Proof Theory of Ordinals( Infinity in Philosophy and Mathematics)}, author={Toshiyasu Arai}, journal={Annals of the Japan Association for Philosophy of Science}, year={2011}, volume={20}, pages={29-47} }

This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and then the latter are analysed. We scarcely touch upon proof theoretical matters.

## 4 Citations

Lifting up the proof theory to the countables : Zermelo-Fraenkel set theory

- Mathematics
- 2011

We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound of definable countable ordinals in the Zermelo-Fraenkel's set theory ZF.

The Use of Trustworthy Principles in a Revised Hilbert’s Program

- Mathematics
- 2015

After the failure of Hilbert’s original program due to Godel’s second incompleteness theorem, relativized Hilbert’s programs have been suggested. While most metamathematical investigations are…

Implicit Dynamic Function Introduction and Ackermann-like FunctionTheory

- PhysicsFLAP
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The paper is based on recollections of Grigori Mints completed by a survey of his research work in a scientific context and sometimes goes beyond the purely scientific aspects to show the atmosphere of these times.

LIFTING PROOF THEORY TO THE COUNTABLE ORDINALS: ZERMELO-FRAENKEL SET THEORY

- Mathematics, PhilosophyThe Journal of Symbolic Logic
- 2014

Abstract We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound on definable countable ordinals in Zermelo-Fraenkel set theory ZF.

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Lifting up the proof theory to the countables : Zermelo-Fraenkel set theory

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We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound of definable countable ordinals in the Zermelo-Fraenkel's set theory ZF.

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