Read more
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.
List of contents
Introduction.- Calculi for classical logic.- Cut-elimination in depth.- Epsilon numbers.- Iterations.- Collapsings.
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.
Report
"Arai's book represents an important contribution to the field of ordinal analysis, and is recommended to any mathematician interested in the classification of the proof-theoretic strength of mathematical theories. ... the book is well written, well organized, and concise ... . Arai is to be commended for this significant resource for anyone who wishes to study ordinal analysis, and gain a better understanding of the proof-theoretic strength of theories." (Matthew Jura, Mathematical Reviews, December, 2023)
