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Decidable Fragments of FirstOrder and FixedPoint Logic  From prefix vocabulary classes to guarded logics
, 2003
"... We survey decidable and undecidable satis ability problems for fragments of rstorder logic and beyond. Classical studies, related to Hilbert's programme and to which Laszlo Kalmar has made important contributions, focussed on pre xvocabulary fragments in rstorder logic; for these a complete ..."
Abstract

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We survey decidable and undecidable satis ability problems for fragments of rstorder logic and beyond. Classical studies, related to Hilbert's programme and to which Laszlo Kalmar has made important contributions, focussed on pre xvocabulary fragments in rstorder logic; for these a complete classi cation of the decidable and undecidable cases has been obtained.
BERNAYS AND SET THEORY
"... Abstract. We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higherorder 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 higherorder 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 twovolume 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 firstorder 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 reevaluation 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 higherorder reflection principles, and produced a stream of
Formal logic
"... Logic studies the validity of arguments. A typical case in point is that of syllogisms: logical arguments in which, starting from two premises, a conclusion is reached. For example, given that There are horses in Spain. ..."
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Logic studies the validity of arguments. A typical case in point is that of syllogisms: logical arguments in which, starting from two premises, a conclusion is reached. For example, given that There are horses in Spain.