Ordinal Analysis with an Introduction to Proof Theory

Beschreibung

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.
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.
Covers ordinal analysis at an advanced level, and proof theory at an elementary level Approaches ordinal analysis in a contemporary fashion Includes a wealth of exercises and answers, making it suitable for student use

Autor*in

Toshiyasu Arai

Themen in »Ordinal Analysis with an Introduction to Proof Theory«

ordinal analysis proof theory ordinals in proof theory consistency proof mathematics of proofs theory of proofs strengths of theories proof theory of first-order arithmetic proof theory of second-order arithmetic proof theory of set theories

Stimmen zu »Ordinal Analysis with an Introduction to Proof Theory«

“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)
()

Details

Link teilen