CiNii Books - Collected works

Kurt Goedel (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to Goedel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Goedel's Nachlass. These long-awaited final two volumes contain Goedel'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 Goedel's Nachlass. 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 Goedel: 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 Goedel'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.

Goedel's life and workSolomon Feferman: A Goedel chronologyJohn W. Dawson, Jr.: Goedel 1929: Introductory note to 1929, 1930 and 1930aBurton Dreben and Jean van Heijenoort: UEber die Vollstandigkeit des Logikkalkuls On the completeness of the calculus of logic Goedel 1930: (See introductory note under Goedel 1929.) Die Vollstandigkeit der Axiome des logischen Funktionenkalkuls The completeness of the axioms of the functional calculus of logic Goedel 1930a: (See introductory note under Goedel 1929.) UEber die Vollstandigkeit des Logikkalkuls On the completeness of the calculus of logic Goedel 1930b: Introductory note to 1930b, 1931 and 1932bStephen C. Kleene: Einige metamathematische Resultate uber Entscheidungs-definitheit und Widerspruchsfreiheit Some metamathematical results on completeness and consistency Goedel 1931: (See introductory note under Goedel 1930b.) UEber formal unentscheidbare Satze der Principia mathematica und verwandter Systeme I On formally undecidable propositions of Principia mathematica and related systems I Goedel 1931a: Introductory note to 1931a, 1932e, f and gJohn W. Dawson, Jr.: Diskussion zur Grundlegung der Mathematik Discussion on providing a foundation for mathematics Goedel 1931b: Review of Neder 1931 Goedel 1931c: Introductory note to 1931cSolomon Feferman: Review of Hilbert 1931 Goedel 1931d: Review of Betsch 1926 Goedel 1931e: Review of Becker 1930 Goedel 1931f: Review of Hasse and Scholz 1928 Goedel 1931g: Review of von Juhos 1930 Goedel 1932: Introductory note to 1932A. S. Troelstra: Zum intuitionistischen aussagenkalkul On the intuitionistic propositional calculus Goedel 1932a: Introductory note to 1932a, 1933i and lWarren D. Goldfarb: Ein Spezialfall des Enscheidungsproblems der theoretischen Logik A special case of the decision problem for theoretical logic Goedel 1932b: (See introductory note under Goedel 1930b.) UEber Vollstandigkeit und Widerspruchsfreiheit On completeness and consistency Goedel 1932c: Introductory note to 1932cW. V. Quine: Eine Eigenschaft der Realisierungen des Aussagenkalkuls A property of the realizations of the propositional calculus Goedel 1932d: Review of Skolem 1931 Goedel 1932e: (See introductory note under Goedel 1931a.) Review of Carnap 1931 Goedel 1932f: (See introductory note under Goedel 1931a.) Review of Heyting 1931 Goedel 1932g: (See introductory note under Goedel 1931a.) Review of von Neumann 1931 Goedel 1932h: Review of Klein 1931 Goedel 1932i: Review of Hoensbroech 1931 Goedel 1932j: Review of Klein 1932 Goedel 1932k: Introductory note to 1932k, 1934e and 1936bStephen C. Kleene: Review of Church 1932 Goedel 1932l: Review of Kalmar 1932 Goedel 1932m: Review of Huntington 1932 Goedel 1932n: Review of Skolem 1932 Goedel 1932o: Review of Dingler 1931 Goedel 1933: Introductory note to 1933W. V. Quine: [[UEber die Parryschen Axiome]] [[On Parry's axioms]] Goedel 1933a: Introductory note to 1933aW. V. Quine: UEber Unabhangigkeitsbeweise im Aussagenkalkul On independence proofs in the propositional calculus Goedel 1933b: Introductory note to 1933b, c, d, g and hJudson Webb: UEber die metrische Einbettbarkeit der Quadrupel des R[3 in Kugelflachen On the isometric embeddability of quadruples of points of R[3 in the surface of a sphere Goedel 1933c: (See introductory note under Goedel 1933b.) UEber die Waldsche Axiomatik des Zwichenbegriffes On Wald's axiomization of the notion of betweenness Goedel 1933d: (See introductory note under Goedel 1933b.) Zur Axiomatik der elementargeometrischen Verknupfungs-relationen On the axiomatization of the relations of connection in elementary geometry Goedel 1933e: Introductory note to 1933eA. S. Troelstra: Zur institutionistischen Arithmetik und Zahlentheorie On intuitionistic arithmetic and number theory Goedel 1933f: Introductory note to 1933fA. S. Troelstra: Eine Interpretation des institutionistischen Aussagenkalkuls An interpretation of the intuitionistic propositional calculus Goedel 1933g: (See introductory note under Goedel 1933b.) Bemerkung uber projektive Abbildungen Remark concerning projective mappings Goedel 1933h: (See introductory note under Goedel 1933b.) Diskussion uber koordinatenlose Differentialgeometrie Discussion concerning coordinate-free differential geometry Goedel 1933i: (See introductory note under Goedel 1932a.) Zum Enscheidungsproblem des logischen Funktionenkalkuls On the decision probelm for the functional calculus of logic Goedel 1933j: Review of Kaczmarz 1932 Goedel 1933k: Review of Lewis 1932 Goedel 1933l: (See introductory note under Goedel 1932a.) Review of Kalmar 1933 Goedel 1933m: Review of Hahn 1932 Goedel 1934: Introductory note to 1934Stephen C. Kleene: On undecidable propositions of formal mathematical systems Goedel 1934a: Review of Skolem 1933 Goedel 1934b: Introductory note to 1934bW. V. Quine: Review of Quine 1933 Goedel 1934c: Introductory note to 1934c and 1935Robert L. Vaught: Review of Skolem 1933a Goedel 1934d: Review of Chen 1933 Goedel 1934e: (See introductory note under Goedel 1932k.) Review of Church 1933 Goedel 1934f: Review of Notcutt 1934 Goedel 1935: (See introductory note under Goedel 1934c.) Review of Skolem 1934 Goedel 1935a: Introductory note to 1935aW. V. Quine: Review of Huntington 1934 Goedel 1935b: Review of Carnap 1934 Goedel 1935c: Review of Kalmar 1934 Goedel 1936: Introductory note to 1936John W. Dawson, Jr.: Diskussionsbemerkung Discussion remark Goedel 1936a: Introductory note to 1936aRohit Parikh: UEber die Lange von Beweisen On the length of proofs Goedel 1936b: (See introductory note under Goedel 1932k.) Review of Church 1935 Textual notes References Index

Kurt Goedel (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 Goedel'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 Goedel's Nachlass. These long-awaited final two volumes contain Goedel'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 Goedel's Nachlass. 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 Goedel: 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 Goedel'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.

Goedel 1938: Introductory note to 1938, 1939, 1939a, and 1940 by Robert M. Solovay
The consistency of the axiom of choice and of the generalized continuum hypothesis
Goedel 1939: the consistency of the generalized continuum hypothesis
Goedel 1939a: Consistency proof for the generalized continuum hypothesis
Goedel 1940: the consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory
Goedel 1944: Introductory note to 1944 by Charles Parsons
Russell's mathematical logic
Goedel 1946: Introductory note to 1946 by Charles Parsons
Remarks before the Princeton bicentennial conference on problems in mathematics
Goedel 1947: Introductory note to 1947 and 1964 by Gregory H. Moore
What is Cantor's continuum problem?
Goedel 1949: Introductory note to 1949 and 1952 by S.W. Hawking
An example of a new type of cosmological solutions of Einstein's field equations of gravitation
Goedel 1949a: Introductory note to 1949a by Howard Stein
A remark about the relationship between relativity theory and idealistic philosophy
Goedel 1952: Rotaoting universes in general relativity theory
Goedel 1958: Introductory note to 1958 and 1972 by A.S. Troelstra
UEber eine bisher noch nicht benutzte Erweiterung des finiten Standpunktes
On a hitherto unutilized extension of the finitary standpoint
Goedel 1962: postscript to Spector 1962
Goedel 1964: What is Cantor's continuum problem? Goedel 1972: On an extension of finitary mathematics which has not yet been used
Goedel 1972a: Introductory note to 1972a by Solomon Feferman, Robert M. Solovay, and Judson C. Webb
Some remarks on the undecidability results
Goedel 1974: Introductory note to 1974 by Jens Erik Fenstad
Remark on non-standard analysis
Textual notes
References.

Kurt Goedel (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 Goedel'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 Goedel's Nachlass. These long-awaited final two volumes contain Goedel'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 Goedel's Nachlass. 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 Goedel: 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 Goedel'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.

1: John W. Dawson, Jr.: The Nachlass of Kurt Goedel: an overview 2: Cheryl A. Dawson: Goedel's Gabelsberger shorthand 3: Warren Goldfarb: Goedel *1930c: Introductory note to *1930c 4: Lecture on completeness of the functional calculus 5: Stephen C. Kleene: Goedel *1931?: Introductory note to *1931? 6: On undecidable sentences 7: Solomon Feferman: Godel *1933c: Introductory note to *1933c 8: The present situation in the foundations of mathematics 9: Israel Halperin: Godel *1933?: Introductory note to *1933? 10: Simplified proof of a theorem of Steinitz 11: Wilfried Sieg and Charles Parsons: Godel *1938a: Introductory note to *1938a 12: Lecture at Zilsel's 13: Robert M. Solovay: Godel *1939b: Introductory note to *1939b and *1940a 14: Lecture at Goettingen 15: Martin Davis: Godel *193?: Introductory note to *193? 16: Undecidable diophantine propositions 17: Godel *1940a 18: Lecture on the consistency of the continuum hypothesis 19: A.S. Troelstra: Godel *1941: Introductory note to *1941 20: In what sense is intuitionistic logic constructive? 21: Howard Stein: Godel *1946/9: Introductory note to *1946/9 22: Some observations about the relationship between theory of relativity and Kantian philosophy 23: David B. Malament: Godel *1949b: Introductory note to *1949b 24: Lecture on rotating universes 25: George Boolos: Godel *1951: Introductory note to *1951 26: Some basic theorems on the foundations of mathematics and their implications 27: Warren Goldfarb: Godel *1953/9: Introductory note to *1953/9 28: Is mathematics syntax of language? Version III 29: Is mathematics syntax of language? Version V 30: Dagfinn Follesdal: Godel *1961/?: Introductory note to *1961/? 31: The modern development of the foundations of mathematics in the light of philosophy 32: Robert M. Adams: Godel *1970: Introductory note to *1970 32: Ontological proof 33: Robert M. Solovay: Godel *1970a: Introductory note to *1970a, *1970b and *1970c 34: Some considerations leading to the probable conclusion that the true power of the continuum is N[2 35: Godel *1970b 36: A proof of Cantor's continuum hypothesis from a highly plausible axiom about orders of growth 37: Godel *1970c 38: Unsent letter to Alfred Tarski Appendix A: Excerpt from *1946/9-A Appendix B: Texts relating to the ontological proof

Kurt Goedel (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 Goedel'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 Goedel's Nachlass. These long-awaited final two volumes contain Goedel'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 Goedel's Nachlass. 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 Goedel: 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 Goedel'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.

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