Kurt Gödel: Results on Foundations
Hämeen-Anttila, Maria, Von Plato, Jan
- 出版商: Springer
- 出版日期: 2024-07-18
- 售價: $6,970
- 貴賓價: 9.5 折 $6,622
- 語言: 英文
- 頁數: 319
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031378776
- ISBN-13: 9783031378775
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商品描述
Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing.
Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old.
The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''
商品描述(中文翻譯)
庫爾特·哥德爾(Kurt Gödel,1906-1978)因其於1931年提出的不完全性定理而聲名遠播。後來,他的目標是解決所謂的希爾伯特第一和第二問題,即關於實數基數的康托爾連續體假設,以及實數和函數理論的一致性。到1940年,他在第一個問題上已經取得了一半的進展,這是他在邏輯和基礎領域的最後一個已發表結果。此後,他對解決這兩個問題的強烈嘗試仍然隱藏在他所有著作中使用的被遺忘的德國速記中。
《基礎結果》(Results on Foundations)是一組於1940年至1942年間撰寫的四本速記筆記,收集了哥德爾認為已完成的結果。其主要主題是集合論,哥德爾在其中預見了數十年的發展。其次,哥德爾完成了他在1933年提出的建立直觀邏輯和模態邏輯之間聯繫的計劃,所用的方法和結果在今天同時是新的和80年前的。
本版哥德爾的四本筆記包含368頁編號頁面和126個編號定理的《基礎結果》,以及哥德爾於1946年準備的74個集合論問題列表,還有一份標題為「我研究的宏大計劃約有一百個問題」的未知日期列表。
作者簡介
Jan von Plato is a Research Director at the University of Helsinki. He has published nine books and numerous articles on foundations of probability, constructive axiomatics, proof theory, and the development of logic and foundational study.
作者簡介(中文翻譯)
Maria Hämeen-Anttila 是芬蘭赫爾辛基大學的博士後研究員。她之前的工作包括編輯《哥德爾:普林斯頓直覺主義講座》,2021年。
Jan von Plato 是赫爾辛基大學的研究主任。他已出版九本書籍以及多篇關於概率基礎、建構公理學、證明理論以及邏輯和基礎研究發展的文章。