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Jerzy Łoś
Jerzy Łoś (born 22 March 1920 in Lwów, Poland (now Lviv, Ukraine) – 1 June 1998 in Warsaw) () was a Polish mathematician, logician, economist, and philosopher. He is especially known for his work in model theory, in particular for "Łoś's theorem", which states that any first-order formula is true in an ultraproduct if and only if it is true in "most" factors (see ultraproduct for details). In model theory he also proved many preservation theorems, but he gave significant contributions, as well, to foundations of mathematics, Abelian group theory and universal algebra. In the 60's he turned his attention to mathematical economics, focusing mainly on production processes and dynamic decision processes. He was faculty at academies in Wrocław, Toruń, and 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lvov
Lviv ( uk, Львів) is the largest city in Western Ukraine, western Ukraine, and the List of cities in Ukraine, 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 Ukrainian culture, cultural centres of Ukraine. It was named in honour of Leo I of Galicia, Leo, the eldest son of Daniel of Galicia, Daniel, King of Ruthenia. Lviv 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 was conquered by King Casimir III the Great of Poland. From 1434, it was the regional capital of the Ruthenian Voivodeship in the Crown of the Kingdom of Poland, 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, f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economist
An economist is a professional and practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are many sub-fields, ranging from the broad philosophy, philosophical theory, theories to the focused study of minutiae within specific Market (economics), markets, macroeconomics, macroeconomic analysis, microeconomics, microeconomic analysis or financial statement analysis, involving analytical methods and tools such as econometrics, statistics, Computational economics, economics computational models, financial economics, mathematical finance and mathematical economics. Professions Economists work in many fields including academia, government and in the private sector, where they may also "study data and statistics in order to spot trends in economic activity, economic confidence levels, and consumer attitudes. They assess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DLMPST
The International Union of History and Philosophy of Science and Technology is one of the members of the International Science Council (ISC). It was founded in 1955 by merging the ''International Union of History of Science'' (IUHS) and the ''International Union of Philosophy of Science'' (IUPS), and consists of two divisions, the ''Division of History of Science and Technology'' (DHST) and the ''Division of Logic, Methodology and Philosophy of Science and Technology'' (DLMPST). Structure and governance The IUHPST does not have its own membership structure and governance, but is an umbrella organisation for its two Divisions, DHST and DLMPST. It is governed by the officers of the two Divisions in a rotational system where the Presidency of the Union rotates between the Presidents of the two Divisions. The current IUHPST President is Nancy Cartwright (President of DLMPST), the current IUHPST Vice President is Marcos Cueto (President of DHST), the current IUHPST Secretary General is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patrick Suppes
Patrick Colonel Suppes (; March 17, 1922 – November 17, 2014) was an American philosopher who made significant contributions to philosophy of science, the theory of measurement, the foundations of quantum mechanics, decision theory, psychology and educational technology. He was the Lucie Stern Professor of Philosophy Emeritus at Stanford University and until January 2010 was the Director of the Education Program for Gifted Youth also at Stanford. Early life and career Suppes was born on March 17, 1922, in Tulsa, Oklahoma. He grew up as an only child, later with a half brother George who was born in 1943 after Patrick had entered the army. His grandfather, C. E. Suppes, had moved to Oklahoma from Ohio. Suppes' father and grandfather were independent oil men. His mother died when he was a young boy. He was raised by his stepmother, who married his father before he was six years old. His parents did not have much formal education.Cf. Suppes autobiography Suppes began college at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toruń
)'' , image_skyline = , image_caption = , image_flag = POL Toruń flag.svg , image_shield = POL Toruń COA.svg , nickname = City of Angels, Gingerbread city, Copernicus Town , pushpin_map = Kuyavian-Pomeranian Voivodeship#Poland#Europe , pushpin_relief=1 , pushpin_label_position = top , subdivision_type = Country , subdivision_name = , subdivision_type1 = Voivodeship , subdivision_name1 = , leader_title = City mayor , leader_name = Michał Zaleski , established_title = Established , established_date = 8th century , established_title3 = City rights , established_date3 = 1233 , area_total_km2 = 115.75 , population_as_of = 31 December 2021 , population_total = 196,935 (16th) Data for territorial unit 0463000. , population_density_km2 = 1716 , population_metro = 297646 , timezone = CET , utc_offset = +1 , timezone_DST = CEST , utc_offset_DST = +2 , coordinates = , elevation_m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wrocław
Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, roughly from the Baltic Sea to the north and from the Sudeten Mountains to the south. , the official population of Wrocław is 672,929, with a total of 1.25 million residing in the metropolitan area, making it the third largest city in Poland. Wrocław is the historical capital of Silesia and Lower Silesia. Today, it is the capital of the Lower Silesian Voivodeship. The history of the city dates back over a thousand years; at various times, it has been part of the Kingdom of Poland, the Kingdom of Bohemia, the Kingdom of Hungary, the Habsburg monarchy of Austria, the Kingdom of Prussia and Germany. Wrocław became part of Poland again in 1945 as part of the Recovered Territories, the result of extensive border changes and expulsions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study. Basic idea In universal algebra, an algebra (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. An ''n''- ary operation on ''A'' is a function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a '' constant'', often denoted by a letter like ''a''. A 1-ary operation (or ''unary operation'') is simply a function from ''A'' to ''A'', often denoted by a symbol placed in front of its argument, like ~''x''. A 2-ary operation (or ''binary operation'') is often denoted by a symbol placed between its argum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation \cdot that combines any two elements a and b of A to form another element of A, denoted a \cdot b. The symbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their model theory, models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematics, metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultraproduct
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equal. For example, ultrapowers can be used to construct new fields from given ones. The hyperreal numbers, an ultrapower of the real numbers, are a special case of this. Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson–Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Predicate Calculus
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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