This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.

Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.

About the Author

Toshiyasu Arai received a PhD from Tsukuba University. His thesis was on an extension of G. Takeuti’s consistency proofs.

He got positions in Nagoya University, Hiroshima University, Kobe University, Chiba University, and University of Tokyo. His research interest is in proof theory. He received the MSJ Autumn Prize from the Mathematical Society of Japan in 2004 for the research on the Hilbert’s second problem.

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