Short description
This second volume of a comprehensive edition of logician Godel's works collects together all his publications from 1938 to 1974. Together with Volume I, it makes available for the first time in a single source all of his previously published work.
Long description
Kurt Godel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Godel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Godel's Nachlass. These long-awaited final two volumes contain Godel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Godel's Nachlass. L All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Godel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Godel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.
Review
... the presentation is impeccable. The introductory notes which explicate Godel's thought are notable papers in themselves ... Such is the thoroughness of the enterprise in making Godel's work accessible, this volume concludes with addenda and corrigenda to Volume I! ... Connoisseurs of mathematical logic and the history and philosophy of mathematics will cherish the opportunity afforded by this volume (and by the first volume, too) to gain insight into the mind of one of the greatest logicians of all time. The Mathematical Gazette The books are carefully and beautifully produced and offer rich material, illuminating not only the outstanding work of Godel, but also the whole mathematical logic of the twentieth century, including some philosophical and historical aspects. EMS
Table of contents
- 1. Introductory Note to 1938, 1939 and 1940
- 2. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis
- 3. CONSISTENCY PROOF FOR THE GENERALIZED CONTINUUM HYPOTHESIS
- 4. The Consistency of the Axiom of Choice and of the Generalized Continuum Hyothesis with the Axioms of Set Theory
- 5. Introductory Note to 1946
- 6. Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics
- 7. Introductory Note to 1947 and 1964
- 8. What is Cantor's Continuum Problem?
- 9. Introductory Note to 1949 and 1952
- 10. An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation
- 11. A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy
- 12. Rotating Universes in General Relativity Theory
- 13. Introductory Note to 1958 and 1972
- 14. On a Hiterto Unutilized Extension of the Finitary Standpoint
- 16. What is Cantor's Continuum problem?
- 17. On an Extension of Finitary Mathematics Which has not Yet Been Used
- 18. Some Remarks on the Undecidability Results
- 19. Introductory Note to 1974
- 20. Remark on Non-Standard Analysis