Mathematical Logic (eBook)

R.O. Gandy, C.E.M. Yates (Autoren)

eBook Download: PDF

2001 | 1. Auflage
306 Seiten
Elsevier Science (Verlag)
978-0-08-053592-0 (ISBN)

Infos

Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.

Inhalt

Front Cover 1
Mathematical Logic 4
Copyright Page 5
Contents 12
Preface 8
Alan Mathison Turing – Chronology 9
Preface to this volume 10
Part I: Computability and Ordinal Logics 14
Chapter 1. Historical Introduction (Solomon Feferman) 16
Chapter 2. 1937 On Computable Numbers, with an Application to the Entscheidungsproblem 22
Chapter 3. 1937 Computability and .-definability. 1937 The p-function in . - K Conversion 70
Chapter 4. 1938 Systems of Logic based on Ordinals 84
Part II: Type Theory 162
Chapter 5. General Introduction to Turing's work on Type Theory 164
Published papers 168
Chapter 6. 1942 (with M.H.A. Newman) A Formal Theorem in Church's Theory of Types 168
Chapter 7. 1942 The Use of Dots as Brackets in Church's System 178
Chapter 8. 1948 Practical Forms of Type Theory 192
Unpublished papers 214
Chapter 9. 1941 Some Theorems about Church's System 214
Chapter 10. 1943–4 Practical Forms of Type Theory II 220
Chapter 11. 1944–5 The Reform of Mathematical Notation 224
Part III: Enigmas, Mysteries and Loose Ends 236
Chapter 12. Turing's Treatise on the Enigma 238
Chapter 13. Turing's Papers on Programming 256
Chapter 14. Excerpt from: Programmer's Handbook for the Manchester Electronic Computer Mark II 264
Chapter 15. Minimum Cost Sequential Analysis Excerpt from unpublished manuscript 268
Chapter 16. The Nature of Turing and the Physical World (Andrew Hodges) 272
Chapter 17. Letter from Robin Gandy to Max Newman 278
Chapter 18. Royal Society Memoir 281
Bibliography 294
Lists of contents of other volumes 302
Appendix: matters arising from other volumes 306

Produkt-Details

• Erscheint lt. Verlag: 5.12.2001
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-053592-5 / 0080535925
• ISBN-13: 978-0-08-053592-0 / 9780080535920