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Studies in Constructive Mathematics and Mathematical Logic : Part I

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概要 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 d...o 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 . . . .続きを見る
目次 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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登録日 2020.06.27
更新日 2020.06.28