Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma.

Biography

Born in

Lemberg 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 o ...

, Austria-Hungary, 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 but continued working in the Underground Warsaw University. After the Warsaw uprising 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 Na ...

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 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 logic 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 s ...

. 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 multili ...

. 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) ''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 Ehrenfeucht (, born 8 August 1932) is a Polish-American mathematician and computer scientist. Life Andrzej Ehrenfeucht formulated the Ehrenfeucht–Fraïssé game, using the back-and-forth method given in Roland Fraïssé's PhD thesis. ...

, 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 Polish set theorists Polish logicians University of Warsaw alumni University of Warsaw faculty 20th-century Polish philosophers Recipients of the State Award Badge (Poland)