Jerzy Łoś (; born 22 March 1920 in Lwów,

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...

(now

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 ...

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

) – 1 June 1998 in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

) was a Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...

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 ...

, and

philosopher Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

. He is especially known for his work in

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 (mat ...

, in particular for "

Łoś's theorem The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof t ...

", which states that any first-order formula is true in an ultraproduct if and only if it is true in "most" factors (see

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 fact ...

for details). In model theory he also proved many preservation theorems, but he gave significant contributions, as well, to

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 theo ...

Abelian group theory Abelian may refer to: Mathematics Group theory * Abelian group, a group in which the binary operation is commutative ** Category of abelian groups (Ab), has abelian groups as objects and group homomorphisms as morphisms * Metabelian group, a gro ...

and

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 stud ...

. In the 60's he turned his attention to

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 diff ...

, focusing mainly on production processes and dynamic decision processes. He was faculty at academies in

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 Eu ...

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 (1975–199 ...

, and

. In 1996, Łoś suffered from a severe brain stroke. He was thenceforward ill until his death in 1998.

Selected publication

* Łoś, Jerzy (1955) Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres. Mathematical interpretation of formal systems, pp. 98–113. North-Holland Publishing Co., Amsterdam.

External links

Jerzy Łoś's biography
1920 births 1998 deaths 20th-century Polish mathematicians 20th-century Polish philosophers Polish logicians Scientists from Lviv {{Poland-mathematician-stub

Selected publication

See also

External links