Overview
- Features a detailed description and explanation of Resultate Grundlagen
- Includes a translation of Gödel's manuscripts from German Gabelsberger shorthand to English
- Illustrates Gödel's attempts to solve Hilbert's first and second problem
Part of the book series: Sources and Studies in the History of Mathematics and Physical Sciences (SHMP)
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Table of contents (3 chapters)
Keywords
About this book
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.''
Editors and Affiliations
About the editors
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.
Bibliographic Information
Book Title: Kurt Gödel: Results on Foundations
Editors: Maria Hämeen-Anttila, Jan von Plato
Series Title: Sources and Studies in the History of Mathematics and Physical Sciences
DOI: https://doi.org/10.1007/978-3-031-37875-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-37874-4Published: 18 July 2023
Softcover ISBN: 978-3-031-37877-5Due: 18 August 2023
eBook ISBN: 978-3-031-37875-1Published: 17 July 2023
Series ISSN: 2196-8810
Series E-ISSN: 2196-8829
Edition Number: 1
Number of Pages: IX, 319
Topics: History of Mathematical Sciences, Mathematical Logic and Foundations