Ordinal Analysis with an Introduction to Proof Theory

Toshiyasu Arai (Autor)

Buch | Hardcover

313 Seiten

2020 | 1st ed. 2020
Springer Verlag, Singapore
978-981-15-6458-1 (ISBN)

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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.

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.

Erscheinungsdatum	14.08.2020
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