Collected Works Volume II: Publications 1938-1974

by Gödel, Kurt; Feferman, S.; Dawson, John W.; Kleene, Stephen C.; Moore, G.; Solovay, R.; van Heijenoort, Jean

• ISBN13: 9780195039726
• ISBN10: 0195039726
• Format: Hardcover
• Copyright: 1989-11-30
• Publisher: Oxford University Press

Summary

Kurt Godel was the most outstanding logician of the twentieth century, famous for his work 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 decisionproblem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past. This second volume of a comprehensive edition of Godel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the formatestablished in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublishedmanuscripts, lectures, correspondence, and extracts from the notebooks. Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic,mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.

Author Biography

The Editor-in-Chief
Solomon Feferman is Professor of Mathematics and Philosophy, and Chairman of the Department of Mathematics at Stanford University. He is past president of the Association of Symbolic Logic.
The Editors
John W. Dawson, Jr., is Professor of Mathematics at Pennsylvania State University, York.
Steven C. Kleene is Emeritus Dean of Letters and Science, and Emeritus Professor of Mathematics and Computer Science at the University of Wisconsin, Madison.
Gregory H. Moore is Associate Professor of Mathematics at McMaster University, Hamilton, Ontario, Canada.
Robert M. Solovay is Professor of Mathematics at the University of California, Berkeley.
The late Jean van Heijenoort was Emeritus Professor of Philosophy at Brandeis University until his death in 1986.

Table of Contents

G÷del 1938: Introductory note to 1938, 1939, 1939a, and 1940

The consistency of the axiom of choice and of the generalized continuum hypothesis

G÷del 1939: the consistency of the generalized continuum hypothesis

G÷del 1939a: Consistency proof for the generalized continuum hypothesis

G÷del 1940: the consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory

G÷del 1944: Introductory note to 1944

Russell's mathematical logic

G÷del 1946: Introductory note to 1946

Remarks before the Princeton bicentennial conference on problems in mathematics

G÷del 1947: Introductory note to 1947 and 1964

What is Cantor's continuum problem?

G÷del 1949: Introductory note to 1949 and 1952

An example of a new type of cosmological solutions of Einstein's field equations of gravitation

G÷del 1949a: Introductory note to 1949a

A remark about the relationship between relativity theory and idealistic philosophy

G÷del 1952: Rotaoting universes in general relativity theory

G÷del 1958: Introductory note to 1958 and 1972

_ber eine bisher noch nicht benntzte Erweiterung des finiten Standpunktes

On a hitherto unutilized extension of the finitary standpoint

G÷del 1962: postscript to Spector 1962

G÷del 1964: What is Cantor's continuum problem?

G÷del 1972: On an extension of finitary mathematics which has not yet been used

G÷del 1972a: Introductory note to 1972a by Solomon Feferman

Some remarks on the undecidability results

G÷del 1974: Introductory note to 1974

Remark on non-standard analysis

Textual notes

References

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