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, mathematical structure, structure, space, Mathematica ...

. He worked primarily in

logic 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 o ...

and

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 ...

and is perhaps best remembered for the Mostowski collapse lemma. He was a member of the

Polish Academy of Sciences The Polish Academy of Sciences (, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of distinguished scholars a ...

and a representative of the Warsaw School of Mathematics.

Biography

Born in Lemberg,

Austria-Hungary Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe#Before World War I, Central Europe between 1867 and 1918. A military ...

, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski 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, also known as the September Campaign, Polish Campaign, and Polish Defensive War of 1939 (1 September – 6 October 1939), was a joint attack on the Second Polish Republic, Republic of Poland by Nazi Germany, the Slovak R ...

but continued working in the Underground Warsaw University. After the

Warsaw uprising The Warsaw Uprising (; ), sometimes referred to as the August Uprising (), or the Battle of Warsaw, was a major World War II operation by the Polish resistance movement in World War II, Polish underground resistance to liberate Warsaw from ...

of 1944, the

Nazis Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...

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. In 1954 Mostowski was awarded by Knight's Cross of the

Order of Polonia Restituta The Order of Polonia Restituta (, ) is a Polish state decoration, state Order (decoration), order established 4 February 1921. It is conferred on both military and civilians as well as on alien (law), foreigners for outstanding achievements in ...

and in 1963 elected a real member of the PAS. After the

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

he supervised Rasiowa's both master and doctoral theses in logic and the foundations of mathematics. 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 ex ...

and undecidability. From 1946 until his death in Vancouver, British Columbia, Canada, he worked at the University of Warsaw. Much of his work, during that time, was on first order

and

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 ...

. He also worked at the State Institute of Mathematics, which was incorporated into the

in 1952. His son Tadeusz is also a mathematician working on

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. With Krzysztof Kurdyka and Adam Parusinski, Tadeusz Mostowski solved René Thom's gradient conjecture in 2000.

Works

Books

* 1968 & 1976: (with Kazimierz Kuratowski) ''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 Mostowski and Czesław Ryll-Nardzewski
"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 Set theorists Polish logicians University of Warsaw alumni Academic staff of the University of Warsaw 20th-century Polish philosophers Recipients of the State Award Badge (Poland)