Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

The debate began when Church proposed to Kurt Gödel that one should define the " effectively computable " functions as the λ-definable functions.

Stephen Kleene ( 1952 ) adds to the list the functions " reckonable in the system S < sub > 1 </ sub >" of Kurt Gödel 1936, and Emil Post's ( 1943, 1946 ) " canonical called normal systems ".

For example, the view that numbers are Platonic objects was revived by Kurt Gödel as a result of certain puzzles that he took to arise from the phenomenological accounts.

The day before Hilbert pronounced these phrases at the 1930 annual meeting of the Society of German Scientists and Physicians, Kurt Gödel — in a roundtable discussion during the Conference on Epistemology held jointly with the Society meetings — tentatively announced the first expression of his incompleteness theorem.

Logical Dilemmas: The Life and Work of Kurt Gödel.

The work of both authors was heavily influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers ( a Gödel numbering ) to logical formulas in order to reduce logic to arithmetic.

Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel.

In letters to his mother, who was not a churchgoer and had raised Kurt and his brother as freethinkers, Gödel argued at length for a belief in an afterlife.

* Kurt Gödel ( 1995 ).

It was first proved by Kurt Gödel in 1929.

* Stanford Encyclopedia of Philosophy: " Kurt Gödel " -- by Juliette Kennedy.

* MacTutor biography: Kurt Gödel.

The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 ( and a rewritten version of the dissertation, published as an article in 1930 ) is not easy to read today ; it uses concepts and formalism that are outdated and terminology that is often obscure.

* Kurt Gödel An example of a new type of cosmological solutions of Einstein ’ s field equations of gravitation Rev.

# REDIRECT Kurt Gödel

Kurt Friedrich Gödel (; ; April 28, 1906 – January 14, 1978 ) was an Austrian American logician, mathematician, and philosopher.

The ancestors of Kurt Gödel were often active in Brünn's cultural life.

The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics.

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency.

" He went on to compare Cohen to Kurt Gödel, saying: " Nothing more dramatic than their work has happened in the history of the subject.

* Absalom is the name of Stephen Kumalo's son in " Lost in the Stars ", Kurt Weil's play based on the novel " Cry the Beloved Country ".

Rise and Fall of the City of Mahagonny () is a political-satirical opera composed by Kurt Weill to a German libretto by Bertolt Brecht.

That it is why neither of them stopped Kurt Marko with their powers.

Barrymore is the godmother of Kurt Cobain and Courtney Love's daughter, Frances Bean Cobain.

Aleksić used the term " Yugo-Dada " and is known to have been in contact with Raoul Hausmann, Kurt Schwitters, and Tristan Tzara.

Ex-soldier Snake Plissken ( Kurt Russell ) is given 24 hours to find the President of the United States, who has been captured after the crash of Air Force One.

" Snake " Plissken ( Kurt Russell ) is escorted to the prison on Manhattan Island by armed officers.

Another version is the Collector's Edition, a two-disc set featuring a remastered transfer with a 5. 1 audio track, two commentaries ( one by John Carpenter and Kurt Russell, another by producer Debra Hill and Joe Alves ), a making-of featurette, the first issue of a comic book series titled John Carpenter's Snake Plissken Chronicles, and a ten-minute deleted opening sequence.

* 1919 – Kurt Eisner, German socialist, is assassinated.

Ram is shot but Veronica misses Kurt, who runs away.

The focus is put on the classical modernist art with the collection of Kurt Schwitters, works of German expressionism, and French cubism, the cabinet of abstracts, the graphics and the department of photography and media.

* The fellowship felt among Hoosiers was referred to in Kurt Vonnegut's book, Cat's Cradle, where it is said that this fellowship is an example of a granfalloon.

* In the science fiction novel The Sirens of Titan by Kurt Vonnegut, a " chronosynclastic infundibulum " is a kind of wormhole through time and space, defined as " where all the different kinds of truths fit together ".

Recently, Brahms scholars Styra Avins and Kurt Hoffman have suggested that this legend is false.

Kurt Walker ( born August 9, 1959 ), professionally known by his stage name Kurtis Blow, is an American rapper and record producer.

Before purchasing any work supposedly by Schwitters, it is best to consult the Kurt Schwitters Archive at the Sprengel Museum in Hannover, Germany.

* 1915 – Lieutenant Kurt Wintgens achieves the first known aerial victory with a synchronized machine-gun armed fighter plane, the Fokker M. 5K / MG Eindecker.

In his family, young Kurt was known as Herr Warum (" Mr. Why ") because of his insatiable curiosity.

Generally known as the " operatic version " of West Side Story, it stars Kiri Te Kanawa as Maria, José Carreras as Tony, Tatiana Troyanos as Anita, Kurt Ollmann as Riff, and Marilyn Horne as the offstage voice who sings " Somewhere ".

Kurt Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic ; such logics are known as intermediate logics.

In any event, Kurt Gödel in 1930 – 31 proved that while the logic of much of PM, now known as first-order logic, is complete, Peano arithmetic is necessarily incomplete if it is consistent.

The earliest known aerial victory with a synchronised machine gun-armed fighter aircraft occurred in 1915, by German Luftstreitkräfte Leutnant Kurt Wintgens.

As a result, Luftwaffe General Kurt Student was put in overall command of developing a paratrooper force to be known as the Fallschirmjäger.

His academic training, particularly in Berlin, put him in contact with well known socialist artists from different traditions, such as Bertolt Brecht, Kurt Weill and Hanns Eisler.

Executive Decision, ( also known as Critical Decision ) is a 1996 action film, directed by Stuart Baird and starring Kurt Russell, Halle Berry, John Leguizamo and Steven Seagal.

Buchrucker's Black Reichswehr took its orders from a secret group in the German Army known as Sondergruppe R comprising Kurt von Schleicher, Eugen Ott, Fedor von Bock and Kurt von Hammerstein-Equord.

Since the early 1980s, Japan has produced a significant output of characteristically harsh bands, sometimes referred to under the portmanteau Japanoise, with perhaps the most well known being Merzbow ( pseudonym for the Japanese noise artist Masami Akita who himself was inspired by the Dada artist Kurt Schwitters's Merz art project of psychological collage ).

On October 22 of that year, in what is known as the Battle of Red Bank, an attack by 900 Hessian troops, serving under British Major General William Howe, who then occupied Philadelphia, was repelled, with heavy losses on the Hessian side ( including the death of their commander, Colonel Carl Emil Kurt von Donop ) by the 600 Continental defenders under Colonel Christopher Greene.

Aberdeen is called the " Gateway to the Olympic Peninsula ", and it is well known for being the hometown of Nirvana members Kurt Cobain and Krist Novoselic, as well as Professional Wrestler Bryan Danielson.

Japanese rock has a vibrant underground rock scene, best known internationally for noise rock bands such as Boredoms and Melt Banana, as well as stoner rock bands such as Boris and alternative acts such as Shonen Knife ( who were championed in the West by Kurt Cobain ), Pizzicato Five and The Pillows ( who gained international attention in 1999 for the FLCL soundtrack ).

In 1932, Kurt Gödel defined a system of Gödel logics intermediate between classical and intuitionistic logic ; such logics are known as intermediate logics.

Many researchers in axiomatic set theory have subscribed to what is known as set-theoretical Platonism, exemplified by mathematician Kurt Gödel.

The French solved this problem when, in late 1914, Roland Garros attached a fixed machine gun to the front of his plane, but while Adolphe Pegoud would become known as the first " ace ", getting credit for five victories, before also becoming the first ace to die in action, it was German Luftstreitkräfte Leutnant Kurt Wintgens, who, on July 1, 1915, scored the very first aerial victory by a purpose-built fighter plane, with a synchronized machine gun.

The Institute is perhaps best known as the academic home of Albert Einstein, John von Neumann, Oskar Morgenstern and Kurt Gödel, after their immigration to the United States.

Some of the best known of the works produced included Norman Mailer's The Naked and the Dead ( 1948 ), Joseph Heller's Catch-22 ( 1961 ) and Kurt Vonnegut Jr .' s Slaughterhouse-Five ( 1969 ).

During the earliest era of air combat in World War I, a small number of frontline German fighter pilots serving with what would become known as the Luftstreitkräfte wore hard bridge pince-nez frames for their corrective lenses, including the very first pilot to defeat an opposing aircraft ( on July 1, 1915 ) using a synchronized machine-gun armed aircraft, Leutnant Kurt Wintgens.

Kurt Lewin played a key role in the evolution of organization development as it is known today.