Andrzej Mostowski (1 November 1913 – 22 August 1975) 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, structure, space, models, and change. History O ...

. He is perhaps best remembered for the Mostowski collapse lemma.

Biography

Born in

Lemberg Lviv ( uk, Львів) is the largest city in western Ukraine, and the 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 cultural centres of Ukraine ...

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of 1 ...

, Mostowski entered

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...

in 1931. He was influenced by

Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, (th ...

, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by

but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German

invasion of Poland The invasion of Poland (1 September – 6 October 1939) was a joint attack on the Republic of Poland by Nazi Germany and the Soviet Union which marked the beginning of World War II. The German invasion began on 1 September 1939, one week aft ...

but continued working in the Underground Warsaw University. After the

Warsaw uprising The Warsaw Uprising ( pl, powstanie warszawskie; german: Warschauer Aufstand) was a major World War II operation by the Polish underground resistance to liberate Warsaw from German occupation. It occurred in the summer of 1944, and it was le ...

of 1944, the

Nazis Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Naz ...

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 Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since ...

and undecidability. From 1946 until his death in

Vancouver, British Columbia Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the most populous city in the province, the 2021 Canadian census recorded 662,248 people in the city, up from 631,486 in 2016. Th ...

, Canada, he worked at the

. Much of his work, during that time, was on first order

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

and

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 st ...

. His son Tadeusz is also a mathematician working on

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilin ...

. With Krzysztof Kurdyka and Adam Parusinski, Tadeusz Mostowski solved

René Thom René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became w ...

's gradient conjecture in 2000.

Works

Books

* 1968 & 1976: (with

Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, (t ...

) ''Set Theory. With an Introduction to Descriptive Set Theory'', Studies in Logic and Foundations of Mathematics #86, North Holland, * 1952: ''Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Godel'', North-Holland, Amsterdam, * 1969: ''Constructible Sets with Applications'', North-Holland, Amsterdam.

Papers

* Andrzej Mostowski
"Über die Unabhängigkeit des Wohlordnungssatzes vom Ordnungsprinzip."
''Fundamenta Mathematicae'' Vol. 32, No.1, ss. 201-252, (1939). * Andrzej Mostowski
"On definable sets of positive integers"
''Fundamenta Mathematicae'' Vol. 34, No. 1, ss. 81-112, (1947). * Andrzej Mostowski
"Un théorème sur les nombres cos 2πk/n"
''Colloquium Mathematicae'' Vol. 1, No. 3, ss. 195-196, (1948). * Casimir Kuratowski, Andrzej Mostowski
"Sur un problème de la théorie des groupes et son rapport à la topologie"
''Colloquium Mathematicae'' Vol. 2, No. 3-4, ss. 212-215, (1951). * Andrzej Mostowski
"Groups connected with Boolean algebras. (Partial solution of the problem P92)"
''Colloquium Mathematicae'' Vol. 2, No. 3-4, ss. 216-219, (1951). * Andrzej Mostowski
"On direct products of theories"
''Journal of Symbolic Logic'', Vol. 17, No. 1, ss. 1-31, (1952). * Andrzej Mostowski
"Models of axiomatic systems"
''Fundamenta Mathematicae'' Vol. 39, No. 1, ss. 133-158, (1952). * Andrzej Mostowski
"On a system of axioms which has no recursively enumerable arithmetic model"
''Fundamenta Mathematicae'' Vol. 40, No. 1, ss. 56-61, (1953). * Andrzej Mostowski
"A formula with no recursively enumerable model"
''Fundamenta Mathematicae'' Vol. 42, No. 1, ss. 125-140, (1955). * Andrzej Mostowski
"Examples of sets definable by means of two and three quantifiers"
''Fundamenta Mathematicae'' Vol. 42, No. 2, ss. 259-270, (1955). * Andrzej Mostowski
"Contributions to the theory of definable sets and functions"
''Fundamenta Mathematicae'' Vol. 42, No. 2, ss. 271-275, (1955). * Andrzej Ehrenfeucht, Andrzej Mostowski
"Models of Axiomatic Theories Admitting Automorphisms"
''Fundamenta Mathematicae'', Vol. 43, No. 1, ss. 50-68 (1956). * Andrzej Mostowski
"L'oeuvre scientifique de Jan Łukasiewicz dans le domaine de la logique mathématique"
''Fundamenta Mathematicae'' Vol. 44, No. 1, ss. 1-11, (1957). * Andrzej Mostowski
"On a generalization of quantifiers"
''Fundamenta Mathematicae'' Vol. 44, No. 1, ss. 12-36, (1957). * Andrzej Mostowski
"On computable sequences"
''Fundamenta Mathematicae'' Vol. 44, No. 1, ss. 37-51, (1957). *

Andrzej Grzegorczyk Andrzej Grzegorczyk (; 22 August 1922 – 20 March 2014) was a Polish logician, mathematician, philosopher, and ethicist noted for his work in computability, mathematical logic, and the foundations of mathematics. Historical family background ...

, Andrzej Mostowski and

Czesław Ryll-Nardzewski Czesław Ryll-Nardzewski (; 7 October 1926 – 18 September 2015) was a Polish mathematician. Born in Wilno, Second Polish Republic (now Vilnius, Lithuania), he was a student of Hugo Steinhaus. At the age of 26 he became professor at Warsaw Univ ...

"The classical and ω-complete arithmetic"
''Journal of Symbolic Logic'' Vol. 23, No. 2, ss. 188-206, (1958). * Andrzej Mostowski
"On a problem of W. Kinna and K. Wagner"
''Colloquium Mathematicae'' Vol. 6, No. 1, ss. 207-208, (1958). * Andrzej Mostowski
"A generalization of the incompleteness theorem"
''Fundamenta Mathematicae'' Vol. 49, No. 2, ss. 205-232, (1961). * Andrzej Mostowski
"Axiomatizability of some many valued predicate calculi"
''Fundamenta Mathematicae'' Vol. 50, No. 2, ss. 165-190, (1961). * Yoshindo Suzuki, Andrzej Mostowski
"On ω-models which are not β-models"
''Fundamenta Mathematicae'' Vol. 65, No. 1, ss. 83-93, (1969).

References

External links

* * Stanislaw Krejewski & Marian Srebrn
On the Life and Work of Andrzek Mostowski
{{DEFAULTSORT:Mostowski, Andrzej 1913 births 1975 deaths Scientists from Lviv 20th-century Polish mathematicians Polish set theorists Polish logicians University of Warsaw alumni University of Warsaw faculty 20th-century Polish philosophers Recipients of the State Award Badge (Poland)