Ordinal Analysis with an Introduction to Proof Theory (Logic in Asia: Studia Logica Library)

"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"--Cover page 4 Front Matter ....Pages i-xvi Introduction (Toshiyasu Arai)....Pages 1-27 Calculi for Classical Logic (Toshiyasu Arai)....Pages 29-64 Cut-Elimination with Depths (Toshiyasu Arai)....Pages 65-96 Epsilon Numbers (Toshiyasu Arai)....Pages 97-173 Iterations (Toshiyasu Arai)....Pages 175-218 Collapsings (Toshiyasu Arai)....Pages 219-290 Answers to Exercises (Toshiyasu Arai)....Pages 291-308 Back Matter ....Pages 309-313