# Andrzej Mostowski

Andrzej Mostowski | |
---|---|

Born | |

Died | 22 August 1975 | (aged 61)

Nationality | Poland |

Alma mater | University of Warsaw |

Known for | Arithmetical hierarchy |

Scientific career | |

Fields | Mathematics |

Institutions | University of Warsaw |

Doctoral advisor | Kazimierz Kuratowski Alfred Tarski |

Doctoral students | Andrzej Ehrenfeucht Moshé Machover Helena Rasiowa Roman Sikorski |

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

## Contents

## Biography[edit]

Born in Lemberg, 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 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.

His son Tadeusz is also a mathematician working on differential geometry.^{[1]} With Krzysztof Kurdyka and Adam Parusinski, Tadeusz Mostowski solved René Thom's gradient conjecture in 2000.

## See also[edit]

## References[edit]

**^**"Archived copy". Archived from the original on 2011-06-13. Retrieved 2010-02-23.CS1 maint: Archived copy as title (link)

## Bibliography[edit]

### Books by Mostowski[edit]

- Kuratowski, Kazimierz; Mostowski, Andrzej (1976) [1968],
*Set theory. With an introduction to descriptive set theory*, Studies in Logic and the Foundations of Mathematics,**86**(Second ed.), Amsterdam-New York-Oxford: North-Holland Publishing Co., MR 0485384 - Andrzej Mostowski,
*Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Godel*, North-Holland, Amsterdam, 1952, ISBN 978-0313231513 - Andrezj Mostowski,
*Constructible Sets with Applications*, North-Holland, Amsterdam, 1969.

### Papers by Mostowski[edit]

- Andrzej Mostowski, "Über die Unabhängigkeit des Wohlordnungssatzes von 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).