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Andrzej Mostowski
Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He worked primarily in logic and foundations of mathematics and is perhaps best remembered for the Mostowski collapse lemma. He was a member of the Polish Academy of Sciences and a representative of the Warsaw School of Mathematics. Biography Born in Lemberg, Austria-Hungary, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German invasion of Poland but continued working in the Underground Warsaw University. After the Warsaw uprising of 1944, the Nazis tried to put him in a concentration camp. With the help of some Polish nurses, he escaped to a hospital, choosing to take bread with him rather than his notebook containing his research. Some of this research he reconstruct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lviv
Lviv ( or ; ; ; see #Names and symbols, below for other names) is the largest city in western Ukraine, as well as the List of cities in Ukraine, fifth-largest city in Ukraine, with a population of It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main Ukrainian culture, cultural centres of Ukraine. Lviv also hosts the administration of Lviv urban hromada. It was named after Leo I of Galicia, the eldest son of Daniel of Galicia, Daniel, King of Ruthenia. Lviv (then Lwów) emerged as the centre of the historical regions of Red Ruthenia and Galicia (Eastern Europe), Galicia in the 14th century, superseding Halych, Chełm, Belz, and Przemyśl. It was the capital of the Kingdom of Galicia–Volhynia from 1272 to 1349, when it went to King Casimir III the Great of Kingdom of Poland, Poland in a Galicia–Volhynia Wars, war of succession. In 1356, Casimir the Great granted it town rights. From 1434, it was the regional capital of the Ruthenian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether an arbitrary program eventually halts when run. Background A decision problem is a question which, for every input in some infinite set of inputs, requires a "yes" or "no" answer. Those inputs can be numbers (for example, the decision problem "is the input a prime number?") or values of some other kind, such as strings of a formal language. The formal representation of a decision problem is a subset of the natural numbers. For decision problems on natural numbers, the set consists of those numbers that the decision problem answers "yes" to. For example, the decision problem "is the input even?" is formalized as the set of even numbers. A decision pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definable set, definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function (mathematics), function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of computational complexity theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the world's countries participated, with many nations mobilising all resources in pursuit of total war. Tanks in World War II, Tanks and Air warfare of World War II, aircraft played major roles, enabling the strategic bombing of cities and delivery of the Atomic bombings of Hiroshima and Nagasaki, first and only nuclear weapons ever used in war. World War II is the List of wars by death toll, deadliest conflict in history, causing World War II casualties, the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Allied-occupied Germany, Germany, Allied-occupied Austria, Austria, Occupation of Japan, Japan, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Polonia Restituta
The Order of Polonia Restituta (, ) is a Polish state decoration, state Order (decoration), order established 4 February 1921. It is conferred on both military and civilians as well as on alien (law), foreigners for outstanding achievements in the fields of education, science, sport, culture, art, economics, national security, national defense, social work, civil service, or for furthering good relations between countries. It is Poland's second-highest civilian state award in the order of precedence, behind the Order of the White Eagle (Poland), Order of the White Eagle. The Order of Polonia Restituta is sometimes regarded as Poland's successor to the ''Order of the Knights of Saint Stanislaus, Bishop and Martyr'', known as the Order of Saint Stanislaus, established in 1765 by Stanisław August Poniatowski, the last King of the Polish–Lithuanian Commonwealth, to honor supporters of the Polish crown. History When Poland regained its independence from the German Empire, Aust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazis
Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During Hitler's rise to power, it was frequently referred to as Hitler Fascism () and Hitlerism (). The term "neo-Nazism" is applied to other far-right groups with similar ideology, which formed after World War II, and after Nazi Germany collapsed. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. Its beliefs include support for dictatorship, fervent antisemitism, anti-communism, anti-Slavism, anti-Romani sentiment, scientific racism, white supremacy, Nordicism, social Darwinism, homophobia, ableism, and the use of eugenics. The ultranationalism of the Nazis originated in pan-Germanism and the ethno-nationalist ''Völkisch movement, Völkisch'' movement which had been a prominent aspect of German nationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw Uprising
The Warsaw Uprising (; ), sometimes referred to as the August Uprising (), or the Battle of Warsaw, was a major World War II operation by the Polish resistance movement in World War II, Polish underground resistance to liberate Warsaw from German occupation. It occurred in the summer of 1944, and it was led by the Polish resistance Home Army (). The uprising was timed to coincide with the retreat of the German forces from Poland ahead of the Soviet advance. While approaching the eastern suburbs of the city, the Red Army halted combat operations, enabling the Germans to regroup and defeat the Polish resistance and to Planned destruction of Warsaw, destroy the city in retaliation. The Uprising was fought for 63 days with little outside support. It was the single largest military effort taken by any European Resistance during World War II, resistance movement during World War II. The defeat of the uprising and suppression of the Home Army enabled the pro-Soviet Polish administra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Underground Education In Poland During World War II
During World War II in Poland, education often took place underground. Secretly conducted education prepared scholars and workers for the postwar reconstruction of Poland and countered German and Soviet threats to eradicate Polish culture. Background: repressions of Polish education After the Polish defeat in the invasion of Poland of 1939 and the subsequent German and Soviet occupation of Polish territory, Poland was divided into the areas directly incorporated into the Reich, areas directly incorporated into the Soviet Union and the German-controlled General Government. According to Nazi racial theories the Slavs needed no higher education and the whole nation was to be turned into uneducated serfs for the German race. The only schools that remained opened were trade schools and courses for factory workers. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invasion Of Poland
The invasion of Poland, also known as the September Campaign, Polish Campaign, and Polish Defensive War of 1939 (1 September – 6 October 1939), was a joint attack on the Second Polish Republic, Republic of Poland by Nazi Germany, the Slovak Republic (1939–1945), Slovak Republic, and the Soviet Union, which marked the beginning of World War II. The German invasion began on 1 September 1939, one week after the signing of the Molotov–Ribbentrop Pact between Germany and the Soviet Union, and one day after the Supreme Soviet of the Soviet Union had approved the pact. The Soviet invasion of Poland, Soviets invaded Poland on 17 September. The campaign ended on 6 October with Germany and the Soviet Union dividing and annexing the whole of Poland under the terms of the German–Soviet Frontier Treaty. The aim of the invasion was to disestablish Poland as a sovereign country, with its citizens destined for The Holocaust, extermination. German and Field Army Bernolák, Slovak forces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Lindenbaum
Adolf Lindenbaum (12 June 1904 – August 1941) was a Polish-Jewish logician and mathematician best known for Lindenbaum's lemma and Lindenbaum–Tarski algebras. Life He was born and brought up in Warsaw. He earned a Ph.D. in 1928 under Wacław Sierpiński and habilitated at the University of Warsaw in 1934. He published works on mathematical logic, set theory, cardinal and ordinal arithmetic, the axiom of choice, the continuum hypothesis, theory of functions, measure theory, point-set topology, geometry and real analysis. He served as an assistant professor at the University of Warsaw from 1935 until the outbreak of war in September 1939. He was Alfred Tarski's closest collaborator of the inter-war period. Around the end of October or beginning of November 1935 he married Janina Hosiasson, a fellow logician of the Lwow–Warsaw school. He and his wife were adherents of logical empiricism, participated in and contributed to the international unity of science move ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw School (mathematics)
Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They published in the journal ''Fundamenta Mathematicae'', founded in 1920—one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski—whose illustrious career would a few years later take him to the University of California, Berkeley—published his celebrated theorem on the undefinability of the notion of truth. Notable members of the Warsaw School of Mathematics have included: * Wacław Sierpiński * Kazimierz Kuratowski * Edward Marczewski * Bronisław Knaster * Zygmunt Janiszewski * Stefan Mazurkiewicz * Stanisław Saks * Karol Borsuk * Roman Sikorski * Nachman Aronszajn * Samuel Eilenberg Additionally, notable logicians of the Lwów–Warsaw School of Logic, working at Warsaw, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
