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"... Abstract. We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles. Paul Isaak Bernays (1888–1977) is an important figure in the development of mathematical logic, being the main bridge between Hilbert and Göd ..."

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Abstract. We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles. Paul Isaak Bernays (1888–1977) is an important figure in the development of mathematical logic, being the main bridge between Hilbert and Gödel in the intermediate generation and making contributions in proof theory, set theory, and the philosophy of mathematics. Bernays is best known for the two-volume 1934,1939 Grundlagen der Mathematik [39, 40], written solely by him though Hilbert was retained as first author. Going into many reprintings and an eventual second edition thirty years later, this monumental work provided a magisterial exposition of the work of the Hilbert school in the formalization of first-order logic and in proof theory and the work of Gödel on incompleteness and its surround, including the first complete proof of the Second Incompleteness Theorem. 1 Recent re-evaluation of Bernays ’ role actually places him at the center of the development of mathematical logic and Hilbert’s program. 2 But starting in his forties, Bernays did his most individuated, distinctive mathematical work in set theory, providing a timely axiomatization and later applying higher-order reflection principles, and produced a stream of

### ISBN 80-86732-84-3 © MATFYZPRESS Ladislav Svante Rieger and his Work in Mathematical Logic and Set Theory

"... Abstract. The present paper is dedicated to Ladislav Svante Rieger (1916–1963), a prominent Czech mathematician who worked in three principal domains: algebra, mathematical logic, and axiomatic set theory. It is a free continuation of the article Kozáková [2005a] in which the personality of L.S. Rie ..."

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Abstract. The present paper is dedicated to Ladislav Svante Rieger (1916–1963), a prominent Czech mathematician who worked in three principal domains: algebra, mathematical logic, and axiomatic set theory. It is a free continuation of the article Kozáková [2005a] in which the personality of L.S. Rieger is introduced and his work in the field of algebra is evaluated. In the following text, we give a brief account on Rieger’s professional life and overview of his research activities and describe his achievements in mathematical logic and axiomatic set theory in more detail. At the end of the paper, we provide the list of Rieger’s most significant publications.