Ordinal Analysis with an Introduction to Proof Theory
Springer Verlag, Singapore
978-981-15-6458-1 (ISBN)
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.
Introduction.- Calculi for classical logic.- Cut-elimination in depth.- Epsilon numbers.- Iterations.- Collapsings.
“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)
Erscheinungsdatum | 14.08.2020 |
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Reihe/Serie | Logic in Asia: Studia Logica Library |
Zusatzinfo | 20 Illustrations, black and white; XVI, 313 p. 20 illus. |
Verlagsort | Singapore |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
Geisteswissenschaften ► Philosophie ► Logik | |
Mathematik / Informatik ► Informatik ► Theorie / Studium | |
Schlagworte | Consistency Proof • mathematics of proofs • ordinal analysis • ordinals in proof theory • Proof theory • proof theory of first-order arithmetic • proof theory of second-order arithmetic • proof theory of set theories • strengths of theories • theory of proofs |
ISBN-10 | 981-15-6458-2 / 9811564582 |
ISBN-13 | 978-981-15-6458-1 / 9789811564581 |
Zustand | Neuware |
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