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Gerhard Gentzen
Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Soviet prison camp in Prague in 1945, having been interned as a German national after the Second World War. Life and career Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non- Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. Gentzen joined the Sturmabteilung in November 1933 although he was by no means compelled to do so. Nevertheless he kept in contact with Bernays until the beginning of the Second World War. In 1935, he corresponded with Abraham Fraenkel in Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greifswald
Greifswald (), officially the University and Hanseatic City of Greifswald (german: Universitäts- und Hansestadt Greifswald, Low German: ''Griepswoold'') is the fourth-largest city in the German state of Mecklenburg-Western Pomerania after Rostock, Schwerin and Neubrandenburg. In 2021 it surpassed Stralsund for the first time, and became the largest city in the Pomeranian part of the state. It sits on the River Ryck, at its mouth into the Danish Wiek (''Dänische Wiek''), a sub-bay of the Bay of Greifswald (''Greifswalder Bodden''), which is itself a sub-bay of the Bay of Pomerania (''Pommersche Bucht'') of the Baltic Sea. It is the seat of the district of Western Pomerania-Greifswald, and is located roughly in the middle between the two largest Pomeranian islands of Rugia (''Rügen'') and Usedom. The closest larger cities are Stralsund, Rostock, Szczecin and Schwerin. It lies west of the River Zarow, the historical cultural and linguistic boundary between West (west of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sturmabteilung
The (; SA; literally "Storm Detachment (military), Detachment") was the original paramilitary wing of the Nazi Party. It played a significant role in Adolf Hitler's rise to power in the 1920s and 1930s. Its primary purposes were providing protection for Nazi rallies and assemblies, disrupting the meetings of opposing parties, fighting against the paramilitary units of the opposing parties, especially the ''Roter Frontkämpferbund'' of the Communist Party of Germany (KPD) and the ''Reichsbanner Schwarz-Rot-Gold'' of the Social Democratic Party of Germany (SPD), and intimidating Romani people, Romani, trade unionists, and especially Jews. The SA were colloquially called Brownshirts () because of the colour of their Uniforms and insignia of the Sturmabteilung, uniform's shirts, similar to Benito Mussolini's blackshirts. The official uniform of the SA was the brown shirt with a brown tie. The color came about because a large shipment of Paul von Lettow-Vorbeck, Lettow-shirts, ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-elimination Theorem
The cut-elimination theorem (or Gentzen's ''Hauptsatz'') is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in his landmark 1934 paper "Investigations in Logical Deduction" for the systems LJ and system LK, LK formalising intuitionistic logic, intuitionistic and classical logic respectively. The cut-elimination theorem states that any judgement that possesses a proof in the sequent calculus making use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use of the cut rule. The cut rule A sequent is a logical expression relating multiple formulas, in the form , which is to be read as proves , and (as glossed by Gentzen) should be understood as equivalent to the truth-function "If (A_1 and A_2 and A_3 …) then (B_1 or B_2 or B_3 …)." Note that the left-hand side (LHS) is a conjunction (and) and the right-hand side (RHS) is a disjunction (or). The LHS may have arbitrarily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Socialist German Lecturers League
The National Socialist German Lecturers League (''Nationalsozialistischer Deutscher Dozentenbund'', also called ''NS-Dozentenbund'' , or abbreviated ''NSDDB''), was a party organization under the NSDAP (the Nazi Party). Origin and purpose The NSDDB emerged in 1935 from the National Socialist Teachers League and was established on the basis of an order of the Deputy Führer Rudolf Hess; its purpose being, the exertion of influence on the universities and the political control of higher education. Massive influence was applied especially on appointments to staff positions.Hentschel, 1996, Appendix C; see the entry for the NSDDB District leaders had a decisive role in the acceptance of an '' Habilitationsschrift'', which was a prerequisite to attaining the rank of ''Privatdozent'' necessary to becoming a university lecturer.Hentschel, 1996, Introduction p. xxxvi ff. The expulsion of the Jewish scientists from the universities was substantially carried out by the activists of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prague Uprising
The Prague uprising ( cs, Pražské povstání) was a partially successful attempt by the Czech resistance movement to liberate the city of Prague from German occupation in May 1945, during the end of World War II. The preceding six years of occupation had fuelled anti-German sentiment and the rapid advance of Allied forces from the Red Army and the United States Army offered the resistance a chance of success. On 5 May 1945, during the end of World War II in Europe, occupying German forces in Bohemia and Moravia were spontaneously attacked by civilians in an uprising, with Czech resistance leaders emerging from hiding to join them. The Russian Liberation Army (ROA), a collaborationist formation of ethnic Russians, defected and supported the insurgents. German forces counter-attacked, but their progress was slowed by barricades constructed by the insurgents. On 8 May, the Czech and German leaders signed a ceasefire allowing all German forces to withdraw from the city, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schutzstaffel
The ''Schutzstaffel'' (SS; also stylized as ''ᛋᛋ'' with Armanen runes; ; "Protection Squadron") was a major paramilitary organization under Adolf Hitler and the Nazi Party in Nazi Germany, and later throughout German-occupied Europe during World War II. It began with a small guard unit known as the ''Saal-Schutz'' ("Hall Security") made up of party volunteers to provide security for party meetings in Munich. In 1925, Heinrich Himmler joined the unit, which had by then been reformed and given its final name. Under his direction (1929–1945) it grew from a small paramilitary formation during the Weimar Republic to one of the most powerful organizations in Nazi Germany. From the time of the Nazi Party's rise to power until the regime's collapse in 1945, the SS was the foremost agency of security, surveillance, and terror within Germany and German-occupied Europe. The two main constituent groups were the ''Allgemeine SS'' (General SS) and '' Waffen-SS'' (Armed SS). Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl-Ferdinands-Universität
) , image_name = Carolinum_Logo.svg , image_size = 200px , established = , type = Public, Ancient , budget = 8.9 billion CZK , rector = Milena Králíčková , faculty = 4,057 , administrative_staff = 4,026 , students = 51,438 , undergrad = 32,520 , postgrad = 9,288 , doctoral = 7,428 , city = Prague , country = Czech Republic , campus = Urban , colors = , affiliations = Coimbra Group EUA Europaeum , website = Charles University ( cs, Univerzita Karlova, UK; la, Universitas Carolina; german: Karls-Universität), also known as Charles University in Prague or historically as the University of Prague ( la, Universitas Pragensis, links=no), is the oldest and largest university in the Czech Republic. It is one of the oldest universities in Europe in continuous operation. Today, the university consists of 17 faculties located in Prague, Hradec Králové, and Plzeň. Charles University belongs among the top three universities in Central and Eastern Europe. It is ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Hitler
Adolf Hitler (; 20 April 188930 April 1945) was an Austrian-born German politician who was dictator of Nazi Germany, Germany from 1933 until Death of Adolf Hitler, his death in 1945. Adolf Hitler's rise to power, He rose to power as the leader of the Nazi Party, becoming the Chancellor of Germany, chancellor in 1933 and then taking the title of in 1934. During his dictatorship, he initiated European theatre of World War II, World War II in Europe by invasion of Poland, invading Poland on 1 September 1939. He was closely involved in military operations throughout the war and was central to the perpetration of the Holocaust: the genocide of Holocaust victims, about six million Jews and millions of other victims. Hitler was born in Braunau am Inn in Austria-Hungary and was raised near Linz. He lived in Vienna later in the first decade of the 1900s and moved to Germany in 1913. He was decorated during his Military career of Adolf Hitler, service in the German Army in Worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hitler Oath
The Hitler Oath (German: or Führer Oath)—also referred in English as the Soldier's Oath—refers to the oaths of allegiance sworn by the officers and soldiers of the German Armed Forces and civil servants of Nazi Germany between the years 1934 and 1945. The oath pledged personal loyalty to Adolf Hitler in place of loyalty to the constitution of the country. Historians view the personal oath of the Third Reich as an important psychological element to obey orders for committing war crimes, atrocities, and genocide. During the Nuremberg trials, many German officers unsuccessfully attempted to use the oath as a defense against charges of war crimes and crimes against humanity. Background During the Weimar era, the oath of allegiance, sworn by the Reichswehr, required soldiers to swear loyalty to the Reich Constitution and its lawful institutions. Following Hitler's appointment as Chancellor in 1933, the military oath changed, the troops now swearing loyalty to people and co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazi Party
The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported the ideology of Nazism. Its precursor, the German Workers' Party (; DAP), existed from 1919 to 1920. The Nazi Party emerged from the extremist German nationalist, racist and populist paramilitary culture, which fought against the communist uprisings in post– World War I Germany. The party was created to draw workers away from communism and into nationalism. Initially, Nazi political strategy focused on anti– big business, anti-bourgeois, and anti-capitalist rhetoric. This was later downplayed to gain the support of business leaders, and in the 1930s, the party's main focus shifted to antisemitic and anti-Marxist themes. The party had little popular support until the Great Depression. Pseudoscientific racist theories were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic. Life Early li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
