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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 "Ultraproduct#Łoś's theorem, Łoś's theorem", which states that any first-order predicate calculus, 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, 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. In 1996, Łoś suffered from a severe brain stroke. He was thenceforward ill until his death in 1998. Selected publication * Łoś, Jerzy ( ... [...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] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), 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 definable set, 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 Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1920 Births
Events January * January 1 ** Polish–Soviet War: The Russian Red Army increases its troops along the Polish border from 4 divisions to 20. ** Kauniainen in Finland, completely surrounded by the city of Espoo, secedes from Espoo as its own market town. * January 7 – Russian Civil War: The forces of White movement, Russian White Admiral Alexander Kolchak surrender in Krasnoyarsk; the Great Siberian Ice March ensues. * January 10 ** The Treaty of Versailles takes effect, officially ending World War I. ** The League of Nations Covenant enters into force. On January 16, the organization holds its first council meeting, in Paris. * January 11 – The Azerbaijan Democratic Republic is recognised de facto by European powers in Palace of Versailles, Versailles. * January 13 – ''The New York Times'' Robert H. Goddard#Publicity and criticism, ridicules American rocket scientist Robert H. Goddard, which it will rescind following the launch of Apollo 11 in 1969. * Janua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dana Scott
Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California. His work on automata theory earned him the Turing Award in 1976, while his collaborative work with Christopher Strachey in the 1970s laid the foundations of modern approaches to the semantics of programming languages. He has also worked on modal logic, topology, and category theory. Early career He received his B.A. in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph.D. thesis on ''Convergent Sequences of Complete Theories'' under the supervision of Alonzo Church while at Princeton, and defended his thesis in 1958. Solomon Feferman (2005) writes of this period: After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960. In 1959, h ... [...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 Marcos Cueto (President of DHST), the current IUHPST Vice President is Valentin Goranko (President of DLMPST), the current IUHPST Secretary General is Liesbeth De Mol ... [...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 nearly 20 years his junior 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 when he was almost six years old. His parents did not have much formal education.Cf. Suppes autob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toruń
Toruń is a city on the Vistula River in north-central Poland and a World Heritage Sites of Poland, UNESCO World Heritage Site. Its population was 196,935 as of December 2021. Previously, it was the capital of the Toruń Voivodeship (1975–1998) and the Pomeranian Voivodeship (1919–1939), Pomeranian Voivodeship (1921–1945). Since 1999, Toruń has been a seat of the local government of the Kuyavian-Pomeranian Voivodeship and is one of its two capitals, together with Bydgoszcz. The cities and neighboring counties form the Bydgoszcz–Toruń twin city metropolitan area. Toruń is one of the oldest cities in Poland; it was first settled in the 8th century and in 1233 was expanded by the Teutonic Knights. For centuries it was home to people of diverse backgrounds and religions. From 1264 until 1411, Toruń was part of the Hanseatic League and by the 17th century a leading trading point, which greatly affected the city's architecture, ranging from Brick Gothic to Mannerism, Mann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wrocław
Wrocław is a city in southwestern Poland, and the capital of the Lower Silesian Voivodeship. It is the largest city and historical capital of the region of Silesia. It lies on the banks of the Oder River in the Silesian Lowlands of Central Europe, roughly from the Sudetes, Sudeten Mountains to the north. In 2023, the official population of Wrocław was 674,132, making it the third-largest city in Poland. The population of the Wrocław metropolitan area is around 1.25 million. Wrocław is the historical capital of Silesia and Lower Silesia. The history of the city dates back over 1,000 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 German Reich, Germany, until it became again part of Poland in 1945 immediately after World War II. Wrocław is a College town, university city with a student population of over 130,000, making it one of the most yo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
Mathematical economics is the application of Mathematics, mathematical methods to represent theories and analyze problems in economics. Often, these Applied mathematics#Economics, applied methods are beyond simple geometry, and may include differential and integral calculus, Recurrence relation, difference and differential equations, Matrix (mathematics), matrix algebra, mathematical programming, or other Computational economics, computational methods.TOC. 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, positiv ... [...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 in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of studythis is the subject of group theory and ring theory in universal algebra, the object of study is the possible types of algebraic structures and their relationships. Basic idea In universal algebra, an (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. Arity 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 ~'' ... [...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 the Norwegian 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 ･ , that combines any two elements a and b of A to form another element of A, denoted a \cdot b. The sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics are the mathematical logic, logical and mathematics, mathematical framework that allows the development of mathematics without generating consistency, self-contradictory theories, and to have reliable concepts of theorems, proof (mathematics), proofs, algorithms, etc. in particular. This may also include the philosophy of mathematics, philosophical study of the relation of this framework with reality. The term "foundations of mathematics" was not coined before the end of the 19th century, although foundations were first established by the ancient Greek philosophers under the name of Aristotle's logic and systematically applied in Euclid's Elements, Euclid's ''Elements''. A mathematical assertion is considered as truth (mathematics), truth only if it is a theorem that is proved from true premises by means of a sequence of syllogisms (inference rules), the premises being either already proved theorems or self-evident assertions called axioms or postulat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
