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BL
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| Record Number
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574511
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b403730
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| Main Entry
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Slisenko, A. O.
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| Title & Author
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Studies in Constructive Mathematics and Mathematical Logic : Part I /\ edited by A. O. Slisenko.
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| Publication Statement
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Boston, MA :: Springer US :: Imprint: Springer,, 1969.
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| Series Statement
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Seminars in Mathematics ;; 4
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| ISBN
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9781468489682
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: 9781468489705
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| Contents
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Method of Establishing Deducibility in Classical Predicate Calculus -- On the Correction of Unprovable Formulas -- Lebesgue Integral in Constructive Analysis -- Sufficient Conditions of Incompleteness for the Formalization of Parts of Arithmetic -- Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols -- Some Reduction Classes and Undecidable Theories -- Deductive Validity and Reduction Classes -- Problem of Decidability for Some Constructive Theories of Equalities -- On Constructive Groups -- Invertible Sequential Variant of Constructive Predicate Calculus -- Choice of Terms in Quantifier Rules of Constructive Predicate Calculus -- Analog of Herbrand's Theorem for Prenex Formulas of Constructive Predicate Calculus -- Variation in the Deduction Search Tactics in Sequential Calculus -- Imbedding Operations Associated with Kripke's 'Semantics' -- On Imbedding Operators -- Undecidability of a Class of Formulas Containing Just One Single-Place Predicate Variable in Modal Calculus -- Sequential Modification of Constructive Logic Calculus for Normal Formulas without Structural Deduction Rules -- On Sequential Modifications of Applied Predicate Calculi -- On Maximal Continuity Regulators for Constructive Functions -- On Representability of Algorithmic ally Decidable Predicates by Rabin Machines.
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| Abstract
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This volume contains a number of short papers reporting results presented to the Leningrad Seminar on Constructive Mathematics or to the Leningrad Seminar on Mathematical Logic. As a rule, the notes do not contain detailed proofs. Complete explanations will be printed in the Trudy (Transac tions) of the V. A. Steklov Mathematics Institute AN SSSR (in the "Problems of Constructive Direction in Mathematics" and the "Mathematical Logic and Logical Calculus" series). The papers published herein are primarily from the constructive direction in mathematics. A. Slisenko v CONTENTS 1 Method of Establishing Deducibility in Classical Predicate Calculus ....... . G. V. Davydov 5 On the Correction of Unprovable Formulas ......... . G. V. Davydov Lebesgue Integral in Constructive Analysis ......... . 9 O. Demuth Sufficient Conditions of Incompleteness for the Formalization of Parts of Arithmetic . . . . . . .. . . 15 N. K. Kosovskii Normal Formfor Deductions in Predicate Calculus with Equality and Functional Symbols. . . . .. . 21 V. A. Lifshits Some Reduction Classes and Undecidable Theories. . . . . . . . . . . . . . . . . . . . . . . .. . . 24 . . . . . . V. A. Lifshits Deductive Validity and Reduction Classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 26 . . . . . . . V. A. Lifshits Problem of Decidability for Some Constructive Theories of Equalities. . . . . . . . . . . . . .. . . 29 . . V. A. Lifshits On Constructive Groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 32 . . . . . . . . . . . V. A. Lifshits Invertible Sequential Variant of Constructive Predicate Calculus. . . . . . . . . . . . .. . . 36 . S. Yu. Maslov Choice of Terms in Quantifier Rules of Constructive Predicate Calculus .. 43 G. E. Mints Analog of Herbrand's Theorem for Prenex Formulas of Constructive Predicate Calculus .. 47 G. E. Mints Variation in the Deduction Search Tactics in Sequential Calculus . . . . . . . . . . . . . . . . .. . . 52 . . . G. E. Mints Imbedding Operations Associated with Kripke's "Semantics" . . . . . . . . . . . . . . . . . . .. . . 60 . . . .
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Science (General).
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| Added Entry
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SpringerLink (Online service)
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