Proof Theory, 2/e (Paperback)

Gaisi Takeuti

  • 出版商: Dover Publications
  • 出版日期: 2013-02-20
  • 售價: $1,100
  • 貴賓價: 9.5$1,045
  • 語言: 英文
  • 頁數: 512
  • 裝訂: Paperback
  • ISBN: 0486490734
  • ISBN-13: 9780486490731
  • 無法訂購

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商品描述

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.

商品描述(中文翻譯)

本書專注於Gentzen型證明理論,詳細概述了作者竹內外史及其他二十世紀邏輯學家的創作。文本探討了證明理論在邏輯及其他數學領域的應用。適合數學的高年級本科生及研究生閱讀,這本早已絕版的專著是數學邏輯及相關主題圖書館的基石。

本書分為三個部分,首先探討一階系統,包括涉及Gentzen的切除定理的謂詞演算及根據哥德爾的不完全性定理和Gentzen的一致性證明來討論自然數的理論。第二部分考慮二階及有限階系統,涵蓋簡單類型理論和無窮邏輯。最後幾章則針對一致性問題,檢視一致性證明及其應用。

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