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Johann Makowsky
Johann (János) A. Makowsky (born March 12, 1948) is a Hungarian-born naturalised Swiss mathematician who works in mathematical logic and the logical foundations of computer science and combinatorics. He studied at ETH Zurich from 1967–73. He was a student in Zürich of Ernst Specker and Hans Läuchli in mathematical logic, (Diploma in Mathematics and Physics 1971, Dr. math.sc. in 1974), of Beno Eckmann (Topology and Geometry) and Volker Strassen (Algorithmics), and in Warsaw of Andrzej Mostowski and Witek Marek, where he spent 1972 as an exchange student. Makowsky held visiting positions at the Banach Center in Warsaw (Poland), Stanford University (USA), Simon Fraser University (Canada), University of Florence (Italy), MIT (USA), Lausanne University and ETH Zurich (Switzerland). He held regular positions at the Free University of Berlin and the Technion – Israel Institute of Technology (Haifa, Israel) where he was a full professor. Among his various contributions are: * In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population of 1,752,286 over a land area of about . Budapest, which is both a city and county, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,303,786; it is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celtic settlement transformed into the Roman town of Aquincum, the capital of Lower Pannonia. The Hungarians arrived in the territory in the late 9th century, but the area was pillaged by the Mongols in 1241–42. Re-established Buda became one of the centres of Renaissance humanist culture by the 15th century. The Battle of Mohács, in 1526, was followed by nearly 150 years of Ottoman rule. After the reconquest of Buda in 1686, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Craig Interpolation
In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, and the two have at least one atomic variable symbol in common, then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic. A stronger form of Craig's interpolation theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem. Example In propositional logic, let ::: \varphi = \lnot(P \land Q) \to (\lnot R \land Q) ::: \psi = (S \to P) \lor (S \to \lnot R) . Then \varphi tautologically implies \psi. This can be verified by writing \varphi in conjunctive normal form: : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categoricity
In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as ''defining'' its model, uniquely characterizing the model's structure. In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories with an infinite model. For example, the second-order Peano axioms are categorical, having a unique model whose domain is the set of natural numbers \mathbb. In model theory, the notion of a categorical theory is refined with respect to cardinality. A theory is -categorical (or categorical in ) if it has exactly one model of cardinality up to isomorphism. Morley's categoricity theorem is a theorem of stating that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities. extended Morley's theorem to uncountable languages: if the language has cardinality and a the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technion – Israel Institute Of Technology
The Technion – Israel Institute of Technology ( he, הטכניון – מכון טכנולוגי לישראל) is a public research university located in Haifa, Israel. Established in 1912 under the dominion of the Ottoman Empire, the Technion is the oldest university in the country. The Technion is ranked as one of the top universities in both Israel and the Middle East, and in the world's top 100 universities in the 2022 Academic Ranking of World Universities. The university offers degrees in science and engineering, and related fields such as architecture, medicine, industrial management, and education. It has 19 academic departments, 60 research centers, and 12 affiliated teaching hospitals. Since its founding, it has awarded more than 123,000 degrees and its graduates are cited for providing the skills and education behind the creation and protection of the State of Israel. Technion's 565 faculty members include three Nobel Laureates in chemistry. Four Nobel Laureates ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free University Of Berlin
The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and the humanities. It is recognised as a leading university in international university rankings. The Free University of Berlin was founded in West Berlin in 1948 with American support during the early Cold War period as a Western continuation of the Friedrich Wilhelm University, or the University of Berlin, whose traditions and faculty members it retained. The Friedrich Wilhelm University (which was renamed the Humboldt University), being in East Berlin, faced strong communist repression; the Free University's name referred to West Berlin's status as part of the Western Free World, in contrast to communist-controlled East Berlin. In 2008, as part of a joint effort, the Free University of Berlin, along with the Hertie School of Governance, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lausanne University
The University of Lausanne (UNIL; french: links=no, Université de Lausanne) in Lausanne, Switzerland was founded in 1537 as a school of Protestant theology, before being made a university in 1890. The university is the second oldest in Switzerland, and one of the oldest universities in the world to be in continuous operation. As of fall 2017, about 15,000 students and 3,300 employees studied and worked at the university. Approximately 1,500 international students attend the university (120 nationalities), which has a wide curriculum including exchange programs with other universities. Since 2005, the university follows the requirements of the Bologna process. The 2011 Times Higher Education World University Rankings ranked the University of Lausanne 116th globally. The CWTS Leiden Ranking 2015 ranks the University of Lausanne 11th in Europe and 41st globally, out of 750 universities. Together with the École polytechnique fédérale de Lausanne (EPFL) the university forms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Florence
The University of Florence (Italian: ''Università degli Studi di Firenze'', UniFI) is an Italian public research university located in Florence, Italy. It comprises 12 schools and has around 50,000 students enrolled. History The first university in Florence was the Studium Generale, which was established by the Florentine Republic in 1321. The Studium was recognized by Pope Clement VI in 1349, and authorized to grant regular degrees. The Pope also established that the first Italian faculty of theology would be in Florence. The Studium became an imperial university in 1364, but was moved to Pisa in 1473 when Lorenzo the Magnificent gained control of Florence. Charles VIII moved it back from 1497 to 1515, but it was moved to Pisa again when the Medici family returned to power. The modern university dates from 1859, when a group of disparate higher-studies institutions grouped together in the Istituto di Studi Pratici e di Perfezionamento, which a year later was recognized as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Fraser University
Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located from downtown Vancouver, was established in 1965 and comprises more than 30,000 students and 160,000 alumni. The university was created in an effort to expand higher education across Canada. SFU is a member of multiple national and international higher education associations, including the Association of Commonwealth Universities, International Association of Universities, and Universities Canada. SFU has also partnered with other universities and agencies to operate joint research facilities such as the TRIUMF, Canada's national laboratory for particle and nuclear physics, which houses the world's largest cyclotron, and Bamfield Marine Station, a major centre for teaching and research in marine biology. Undergraduate and graduate programs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considered among the most prestigious universities in the world. Stanford was founded in 1885 by Leland and Jane Stanford in memory of their only child, Leland Stanford Jr., who had died of typhoid fever at age 15 the previous year. Leland Stanford was a U.S. senator and former governor of California who made his fortune as a railroad tycoon. The school admitted its first students on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after the death of Leland Stanford in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, provost of Stanford Frederick Terman inspired and supported faculty and graduates' entrepreneu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor W
The name Victor or Viktor may refer to: * Victor (name), including a list of people with the given name, mononym, or surname Arts and entertainment Film * ''Victor'' (1951 film), a French drama film * ''Victor'' (1993 film), a French short film * ''Victor'' (2008 film), a 2008 TV film about Canadian swimmer Victor Davis * ''Victor'' (2009 film), a French comedy * ''Victor'', a 2017 film about Victor Torres by Brandon Dickerson * ''Viktor'' (film), a 2014 Franco/Russian film Music * ''Victor'' (album), a 1996 album by Alex Lifeson * "Victor", a song from the 1979 album ''Eat to the Beat'' by Blondie Businesses * Victor Talking Machine Company, early 20th century American recording company, forerunner of RCA Records * Victor Company of Japan, usually known as JVC, a Japanese electronics corporation originally a subsidiary of the Victor Talking Machine Company ** Victor Entertainment, or JVCKenwood Victor Entertainment, a Japanese record label ** Victor Interactive So ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
