[BOOK][B] On formally undecidable propositions of Principia Mathematica and related systems
K Gödel - 1992 - books.google.com
In 1931, a young Austrian mathematician published an epoch-making paper containing one
of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered
detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are …
of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered
detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are …
An example of a new type of cosmological solutions of Einstein's field equations of gravitation
K Gödel - Reviews of modern physics, 1949 - APS
All cosmological solutions with non-vanishing den-sity of matter known at present'have the
com-mon property that, in a certain sense, they contain an" absolute" time coordinate,'owing
to the fact that there exists a one-parametric system of three-spaces everywhere orthogonal …
com-mon property that, in a certain sense, they contain an" absolute" time coordinate,'owing
to the fact that there exists a one-parametric system of three-spaces everywhere orthogonal …
CONSISTENCY-PROOF FOR THE GENERALIZED CONTINUUM-HYPOTHESIS
K Gödel - Mathematical Logic In The 20th Century, 2003 - World Scientific
Abstract If M is an arbitrary domain of things in which a binary relation ε is defined, call
“propositional function over M” any expression φ containing (besides brackets) only the
following symbols: 1. Variables x, y…. whose range is M. 2. Symbols a1… an denoting2 …
“propositional function over M” any expression φ containing (besides brackets) only the
following symbols: 1. Variables x, y…. whose range is M. 2. Symbols a1… an denoting2 …
[BOOK][B] Kurt Gödel: Collected Works: Volume III: Unpublished Essays and Lectures
K Gödel, S Feferman - 1986 - books.google.com
Kurt Gödel (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 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 …
Russell's mathematical logic
K Gödel - 1944, 1944 - books.google.com
Mathematical logic, which is nothing else but a precise and complete formulation of formal
logic, has two quite different aspects. On the one hand, it is a section of Mathematics treating
of classes, relations, combinations of symbols, etc., instead of numbers, functions, geometric …
logic, has two quite different aspects. On the one hand, it is a section of Mathematics treating
of classes, relations, combinations of symbols, etc., instead of numbers, functions, geometric …
[CITATION][C] An Example of a new type of cosmological solutions of Einstein's field equations of graviation
K Godel - Rev. Mod. Phys., 1949 - inspirehep.net
… An Example of a new type of cosmological solutions of Einstein's field equations of graviation.
Kurt Godel (Princeton, Inst. Advanced Study) 1949 - 4 pages. Rev.Mod.Phys. 21 (1949) 447-450;
DOI: 10.1103/RevModPhys.21.447. Record added 2001-03-08, last modified 2015-12-09 …
Kurt Godel (Princeton, Inst. Advanced Study) 1949 - 4 pages. Rev.Mod.Phys. 21 (1949) 447-450;
DOI: 10.1103/RevModPhys.21.447. Record added 2001-03-08, last modified 2015-12-09 …
[BOOK][B] The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory
K Godel, GW Brown - 1940 - pdfs.semanticscholar.org
CHAPTER I. THE AXIOMS OF ABSTRACT SET THEORY.. 3 CHAPTER II. EXISTENCE OF
CLASSES AND SETS.... 8 CHAPTER III. ORDINAL NUMBERS.. 21 CHAPTER IV.
CARDINAL NUMBERS 30 CHAPTER V. THE MODEL 35 CHAPTER VI. PROOF OF THE …
CLASSES AND SETS.... 8 CHAPTER III. ORDINAL NUMBERS.. 21 CHAPTER IV.
CARDINAL NUMBERS 30 CHAPTER V. THE MODEL 35 CHAPTER VI. PROOF OF THE …
What is Cantor's continuum problem?
K Godel - The American Mathematical Monthly, 1947 - JSTOR
This question, of course, could arise only after the concept of" number" had been extended
to infinite sets; hence it might be doubted if this extension can be effected in a uniquely
determined manner and if, therefore, the statement of the problem in the simple terms used …
to infinite sets; hence it might be doubted if this extension can be effected in a uniquely
determined manner and if, therefore, the statement of the problem in the simple terms used …
[CITATION][C] What is Cantor's continuum problem
K Gödel - Philosophy of mathematics: selected …, 1964 - Englewood Cliffs: Prentice Hall
[CITATION][C] Some basic theorems on the foundations of mathematics and their implications
K Godel - Collected Words, 1995 - ci.nii.ac.jp
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