In Memory of Andrzej Mostowski
[From Studia Logica 37(1977).1-2, pp. 1-3]
Andrzej Mostowski (1913-1975), one of the most distinguished Polish mathematicians and logicians, was the leading spirit of the Polish school of logic and the foundations of mathematics after the second world war.
Born in Lwów in November 1, 1913, he spent most of his life in Warsaw. He studied mathematics at the University of Warsaw in the years 1931-1936. Outstanding mathematicians and logicians of this environment - cofounders of the Polish schools of mathematics, foundations of mathematics and logic - in particular Wacław Sierpiński, Stefan Mazurkiewicz, Kazimierz Kuratowski, Jan Łukasiewicz and Alfrad Tarski, were his teachers. The strongest influence on the research interests of Andrzej Mostowski was exercised by his principal teacher Alfred Tarski.
In the years 1936, 1937 he continued his studies of mathematics in Vienna and in Zürich. In Vienna he was a student of Kurt Gödel. He renewed contacts with Gödel in the academic year 1948/1949 being at that time a member of the Institute for Advanced Studies in Princeton. Contacts with Gödel and his works strongly influenced Mostowski's research concerned with the foundations of arithmetic and of set theory.
In 1939, at the University of Warsaw, he obtained his Ph.D. on the basis of a doctoral thesis devoted to varous forms of the definition of finiteness of a set. In 1945 Andrzej Mostowski was habilitated at the Jagiellonian University in Cracow. His dissertation was concerned with the independence of the axiom of choice, initating research on the independence of various forms of the axiom of choice for finite sets.
He then returned to Warsaw and took charge of the Department of Philosophy of Mathematics at the University of Warsaw and remained its head till 1953. In the years 1953-1969 he fulfilled duties of head of the Department of Algebra, and from 1969 till his death Professor Mostowski was head of the Department of the Foundations of Mathematics. His intensive research and teaching activities were not confined to the University. From the opening of the State Mathematical Institute in 1949, later transformed into Mathematical Institute of the Polish Academy of Sciences, Professor Mostowski was head of the Section concerned with the Foundations of Mathematics in this Institute.
A great contribution of Professor Mostowski to Polish science was the creation of a cadre of specialists in the foundations of mathematics and mathematical logic and the inspiring influence he exercised on their research. The awaking of interest in modern branches of algebra in Poland was also in a considerable measure due to Andrzej Mostowski. The algebra textbooks written by him jointly with Marceli Stark were used for many years as fundamental teaching manuals and are still recomended to students.
Andrzej Mostowski also found time to participate in international scientific activities. He kept in touch with many distinguished specialists in the world. These contacts enabled him to learn about the most interesting results before their publications, directly from the authors, and problems being curently the center of interest. Young specialists from all over the world came to work with him. He was invited to give invited adresses at many international symposia and congresses and to lecture at many universities and research centres.
In 1956 Andrzej Mostowski was elected a corresponding member and in 1963 a full member of the Polish Academy of Sciences. In 1973 he became a member of the Finnish Academy of Sciences. For his mathematical achievements he was awarded two state prizes and also a prize of Irzykowski Foundation, which is an American foundation for promoting the work of distinguished Polish scientists.
Professor Mostowski fulfilled many administrative functions in various Polish institutions concerned with sciences and higher learning, and Polish scientific societies. He also fulfilled a number of functions in the administration of the Association for Symbolic Logic. In the years 1964-1968 he was Vice-President and from 1971 to 1975 the President of Division of Logic, Methodology and Philosophy of Science of the International Union of the History and Philosophy of Science.
Professor Mostowski also fulfilled many editorial duties. He was the editor of the Mathematical, Astronomical and Physical series of the Bulletin of the Polish Academy of Sciences, a member of the editorial commitees of Fundamenta Mathematicae, Dissertationes Mathematicae, the Journal of Symbolic Logic and others. He was one of the editors of the North-Holland series Studies in Logic and the Foundations of Mathematics, and also one of the founders and editors of the Annals of Mathematical Logic. Professor Mostowski was also a member of the editorial board of Studia Logica.
Andrzej Mostowski left behind him 118 scientific publications, comprising monographs, textbooks and expository works, which form a lasting contribution to the Polish and world science.
During the whole period of his research activity Mostowski carried on studies concerned with the foundations of set theory. His works and results contained in them are fundamental in this field. Investigations of decidability, recursion and hierarchy of arithmetical notions, carried on by Mostowski till 1958, constituted another intensive stream of his research and led to achievements of permanent value for the development of metamathematics and the foundations of mathematics. The last seventeen years of Mostowski's research activity were in a considerable measure devoted to studies concerned with second-order arithmetic and its models ($\omega$-models and $\beta$-models). His works opened up new lines of investigation and are fundamental for the development of this branch of the foundations of mathematics.
The theory of models was treated by Andrzej Mostowski as a tool to investigate other branches of the foundations of mathematics. In spite of this point of view his results in this field contained in several papers (1952-1968) exercised an important influence on the development of model theory. The notions and methods introduced in these papers are among employed in monographs and textbooks.
Logical calculi were investigated by Andrzej Mostowski in a number of papers written in the years 1948-1963. Three of them were concerned with many-valued logics. The first (1961) presents an example of a non-axiomatizable many-valued logic. In the second (1961) axiomatizability of some many-valued predicate calculi is established. The third paper (1963) is devoted to the Hilbert epsilon function in many-valued logics.
An inspiring role for metamathematical studies of classical and non-classical predicate calculi was played by Mostowski's paper "Proofs of non-deducibility in intuitionistic functional calculus" (JSL, 1948), in which an idea of algebraic interpretations of formulas of intuitionistic predicate calculi was suggested. This idea was modified and extended on to classical and various non-classical predicate calculi by other authors and was the source of their research on an algebraic approach to these calculi. In particular it was a starting point for studies leading to "The Mathematics of Metamathematics" written by the editor of this volume of Studia Logica [Helena Rasiowa] jointly with Roman Sikorski.
In the light of what has been said above this volume of Studia Logica is dedicated to the memory of Andrzej Mostowski.
Warsaw, November 1976
Helena Rasiowa
Bibliography of Andrzej Mostowski's works
See also The Mathematics Genealogy Project and The MacTutor History of Mathematics archive.
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