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Wanda Szmielew
Wanda Szmielew née Montlak (5 April 1918 – 27 August 1976) was a Polish mathematical logician who first proved the decidability of the first-order theory of abelian groups. Life Wanda Montlak was born on 5 April 1918 in Warsaw. She completed high school in 1935 and married, taking the name Szmielew. In the same year she entered the University of Warsaw, where she studied logic under Adolf Lindenbaum, Jan Łukasiewicz, Kazimierz Kuratowski, and Alfred Tarski. Her research at this time included work on the axiom of choice, but it was interrupted by the 1939 Invasion of Poland. Szmielew became a surveyor during World War II, during which time she continued her research on her own, developing a decision procedure based on quantifier elimination for the theory of abelian groups. She also taught for the Polish underground. After the liberation of Poland, Szmielew took a position at the University of Łódź, which was founded in May 1945. In 1947, she published her paper on the a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officially estimated at 1.86 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 7th most-populous city in the European Union. The city area measures and comprises 18 districts, while the metropolitan area covers . Warsaw is an Alpha global city, a major cultural, political and economic hub, and the country's seat of government. Warsaw traces its origins to a small fishing town in Masovia. The city rose to prominence in the late 16th century, when Sigismund III decided to move the Polish capital and his royal court from Kraków. Warsaw served as the de facto capital of the Polish–Lithuanian Commonwealth until 1795, and subsequently as the seat of Napoleon's Duchy of Warsaw. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom Of Choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family (S_i)_ of nonempty sets, there exists an indexed set (x_i)_ such that x_i \in S_i for every i \in I. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. In many cases, a set arising from choosing elements arbitrarily can be made without invoking the axiom of choice; this is, in particular, the case if the number of sets from which to choose the elements is finite, or if a canonical rule on how to choose the elements is available – some distinguishin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1918 Births
This year is noted for the end of the World War I, First World War, on the eleventh hour of the eleventh day of the eleventh month, as well as for the Spanish flu pandemic that killed 50–100 million people worldwide. Events Below, the events of World War I have the "WWI" prefix. January * January – 1918 flu pandemic: The "Spanish flu" (influenza) is first observed in Haskell County, Kansas. * January 4 – The Finnish Declaration of Independence is recognized by Russian Soviet Federative Socialist Republic, Soviet Russia, Sweden, German Empire, Germany and France. * January 9 – Battle of Bear Valley: U.S. troops engage Yaqui people, Yaqui Native American warriors in a minor skirmish in Arizona, and one of the last battles of the American Indian Wars between the United States and Native Americans. * January 15 ** The keel of is laid in Britain, the first purpose-designed aircraft carrier to be laid down. ** The Red Army (The Workers and Peasants Red Army) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamenta Mathematicae
''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems. Originally it only covered topology, set theory, and foundations of mathematics: it was the first specialized journal in the field of mathematics..... It is published by the Mathematics Institute of the Polish Academy of Sciences. History The journal was conceived by Zygmunt Janiszewski as a means to foster mathematical research in Poland.According to and to the introduction to the 100th volume of the journal (1978, pp=1–2). These two sources cite an article written by Janiszewski himself in 1918 and titled "''On the needs of Mathematics in Poland''". Janiszewski required that, in order to achieve its goal, the journal should not force Polish mathematicians to submit articles written exclusively in Polish, and should be devoted ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karol Borsuk
Karol Borsuk (May 8, 1905 – January 24, 1982) was a Polish mathematician. His main interest was topology, while he obtained significant results also in functional analysis. Borsuk introduced the theory of '' absolute retracts'' (ARs) and ''absolute neighborhood retracts'' (ANRs), and the cohomotopy groups, later called Borsuk– Spanier cohomotopy groups. He also founded shape theory. He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge. His topological and geometric conjectures and themes stimulated research for more than half a century; in particular, his open problems stimulated the infinite-dimensional topology. Borsuk received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively; his PhD thesis advisor was Stefan Mazurkiewicz. He was a member of the Polish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Geometry
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play. Axiomatic systems Based on ancient Greek methods, an ''axiomatic system'' is a formal description of a way to establish the ''mathematical truth'' that flows from a fixed set of assumptions. Although applicable to any area of mathematics, geometry is the branch of elementary ... [...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] |
Solomon Feferman
Solomon Feferman (December 13, 1928 – July 26, 2016) was an American philosopher and mathematician who worked in mathematical logic. Life Solomon Feferman was born in The Bronx in New York City to working-class parents who had immigrated to the United States after World War I and had met and married in New York. Neither parent had any advanced education. The family moved to Los Angeles, where Feferman graduated from high school at age 16. He received his B.S. from the California Institute of Technology in 1948, and in 1957 his Ph.D. in mathematics from the University of California, Berkeley, under Alfred Tarski, after having been drafted and having served in the U.S. Army from 1953 to 1955. In 1956 he was appointed to the Departments of Mathematics and Philosophy at Stanford University, where he later became the Patrick Suppes Professor of Humanities and Sciences. Feferman died on 26 July 2016 at his home in Stanford, following an illness that lasted three months and a stroke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studia Logica
''Studia Logica'' (full name: Studia Logica, An International Journal for Symbolic Logic), is a scienific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all scientific disciplines; the key criterion for published papers is not their topic but their method: they are required to contain significant and original results concerning formal systems and their properties. The journal offers papers on topics in general logic and on applications of logic to methodology of science, linguistics, philosophy, and other branches of knowledge. The journal is published by the Institute of Philosophy and Sociology of the Polish Academy of Sciences and Springer publications. History The name Studia Logica appeared for the first time in 1934, but only one volume (edited by Jan Łukasiewicz) has been published that time. It had been published continuously since December 1953 in changing frequency by the Polish Acade ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Łódź
The University of Łódź (Polish: ''Uniwersytet Łódzki'', Latin: ''Universitas Lodziensis'') is a public research university founded in 1945 in Łódź, Poland, as a continuation of three higher education institutions functioning in Łódź in the interwar period — the Teacher Training Institute (1921–1928), the Higher School of Social and Economic Sciences (1924–1928) and the local division of the Free Polish University of Warsaw (1928–1939). The University of Łódź (alternative spelling: University of Lodz) is a fully accredited, state-owned, traditional university. It is one of 18 institutions of its type in Poland. It has more than 25,000 students and 2,600 teachers. Its international cooperation includes 385 partner institutions from all over the world. A range of BA, MA, and postgraduate courses held in English as a language of instruction are offered to Polish and overseas students. Reputation The university strives to maintain its high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier Elimination
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement "\exists x such that \ldots" can be viewed as a question "When is there an x such that \ldots?", and the statement without quantifiers can be viewed as the answer to that question. One way of classifying formulas is by the amount of quantification. Formulas with less depth of quantifier alternation are thought of as being simpler, with the quantifier-free formulas as the simplest. A theory has quantifier elimination if for every formula \alpha, there exists another formula \alpha_ without quantifiers that is equivalent to it ( modulo this theory). Examples An example from high school mathematics says that a single-variable quadratic polynomial has a real root if and only if its discriminant is non-negative: :: \exists x\in\mathbb. (a\neq 0 \wedge ax^2+bx+c=0)\ \ \Longleftrightarrow\ \ a\neq 0 \wedge b^2-4ac\geq 0 He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Procedure
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?". The answer is either 'yes' or 'no' depending upon the values of ''x'' and ''y''. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem. A decision procedure for the decision problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?" would give the steps for determining whether ''x'' evenly divides ''y''. One such algorithm is long division. If the remainder is zero the answer is 'yes', otherwise it is 'no'. A decision problem which can be solved by an algorithm is called ''decidable''. Decision problems typically appear in ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
