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Andrzej Mostowski
Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma. 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 reconstructed after the War, however much of it remained lost. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lviv
Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukraine. It was named in honour of Leo, the eldest son of Daniel, King of Ruthenia. Lviv emerged as the centre of the historical regions of Red Ruthenia and 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 was conquered by King Casimir III the Great of Poland. From 1434, it was the regional capital of the Ruthenian Voivodeship in the Kingdom of Poland. In 1772, after the First Partition of Poland, the city became the capital of the Habsburg Kingdom of Galicia and Lodomeria. In 1918, for a short time, it was the capital of the West Ukrainian People's Republic. Between the wars, the city was the centre of the Lwów Voivodeship in th ... [...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. 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 movement, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Thom
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Erik Christopher Zeeman). Life and career René Thom grow up in a modest family in Montbéliard, Doubs and obtained a Baccalauréat in 1940. After German invasion of France, his family took refuge in Switzerland and then in Lyon. In 1941 he moved to Paris to attend Lycée Saint-Louis and in 1943 he began studying mathematics at École Normale Supérieure, becoming agrégé in 1946. He received his PhD in 1951 from the University of Paris. His thesis, titled ''Espaces fibrés en sphères et carrés de Steenrod'' (''Sphere bundles and Steenrod squares''), was w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adam Parusinski
Adam; el, Ἀδάμ, Adám; la, Adam is the name given in Genesis 1-5 to the first human. Beyond its use as the name of the first man, ''adam'' is also used in the Bible as a pronoun, individually as "a human" and in a collective sense as "mankind". tells of God's creation of the world and its creatures, including ''adam'', meaning humankind; in God forms "Adam", this time meaning a single male human, out of "the dust of the ground", places him in the Garden of Eden, and forms a woman, Eve, as his helpmate; in Adam and Eve eat the fruit of the tree of knowledge and God condemns Adam to labour on the earth for his food and to return to it on his death; deals with the birth of Adam's sons, and lists his descendants from Seth to Noah. The Genesis creation myth was adopted by both Christianity and Islam, and the name of Adam accordingly appears in the Christian scriptures and in the Quran. He also features in subsequent folkloric and mystical elaborations in later Judaism, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krzysztof Kurdyka
Krzysztof () is a Polish given name, equivalent to English ''Christopher''. The name became popular in the 15th century. Its diminutive forms include Krzyś, Krzysiek, and Krzysio; augmentative – Krzychu Individuals named Krzysztof may choose to celebrate their name day on March 15, July 25, March 2, May 21, August 20 or October 31. People with the first name Krzysztof * Krzysztof Arciszewski (1592–1656), Polish military man * Krzysztof Bednarski (born 1953), famous contemporary Polish sculptor * Krzysztof Bizacki (born 1973), Polish footballer * Krzysztof Bukalski (born 1970), Polish footballer * Krzysztof Charamsa (born 1972), Polish priest * Krzysztof Chodkiewicz, d. 1652, Polish-Lithuanian nobleman * Krzysztof Cwalina (born 1971), Polish freestyle swimmer * Krzysztof Czerwinski (Krzysztof Czerwiński) (born 1980), Polish conductor, organist and voice teacher * Krzysztof Dabrowski (Krzysztof Dąbrowski) (born 1978), Polish footballer * Krzysztof Głowacki (born 1986), Pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tadeusz Mostowski (mathematician)
Tadeusz Antoni Mostowski (19 October 1766, Warsaw - 6 December 1842, Paris) was a Polish writer, journalist, literary critic and politician. Biography He was the son of , a noted military commander. He was raised in an intellectual atmosphere and studied at the Collegium Nobilium. In 1780, he became an Assessor and was later elected a member of the Great Sejm. In 1790, he was a Podstoli for the Masovian Voivodeship and also became a Castellan in Raciąż, thereby gaining a place in the . He was a supporter of the Patriotic Party and helped create the Friends of the Constitution. In 1792, together with Julian Ursyn Niemcewicz and , he published the '. During the period of the Targowica Confederation he left Poland; eventually arriving in Paris, where he became a mediator in talks between Polish emigrants and French revolutionary authorities. After the defeat of the Girondists, he was imprisoned but soon released and allowed to return home. There, he found himself persecuted an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...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 arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...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 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 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 subrecursive hierarchies, formal methods, and formal languages. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazis
Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Nazi Germany. During Hitler's rise to power in 1930s Europe, it was frequently referred to as Hitlerism (german: Hitlerfaschismus). The later related term "neo-Nazism" is applied to other far-right groups with similar ideas which formed after the Second World War. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. It incorporates a dictatorship, fervent antisemitism, anti-communism, scientific racism, and the use of eugenics into its creed. Its extreme nationalism originated in pan-Germanism and the ethno-nationalist '' Völkisch'' movement which had been a prominent aspect of German nationalism since the late 19th century, and it was strongly influenced by the paramilitary groups that emerged af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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