Ordinal Analysis with an Introduction to Proof Theory

Ordinal Analysis with an Introduction to Proof Theory
PDF, ePUB
  • eBook:
    Ordinal Analysis with an Introduction to Proof Theory
  • Author:
    Toshiyasu Arai
  • Edition:
    1st ed. 2020 edition
  • Categories:
  • Data:
    August 12, 2020
  • ISBN:
    9811564582
  • ISBN-13:
    9789811564581
  • Language:
    English
  • Pages:
    329 pages
  • Format:
    PDF, ePUB

Book Description
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.

Content

1. Introduction
2. Calculi for Classical Logic
3. Cut-Elimination with Depths
4. Epsilon Numbers
5. Iterations
6. Collapsings
7. Answers to Exercises

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