Studies in Constructive Mathematics and Mathematical Logic: Part I
A. O. Slisenko
ΠΌΠ°Ρ 2013. Β· Mechanics: Analysis 1. ΠΊΡΠΈΠ³Π° Β· Springer Science & Business Media
Π-ΠΊΡΠΈΠ³Π°
88
Π‘ΡΡΠ°Π½ΠΈΡΠ°
reportΠΡΠ΅Π½Π΅ ΠΈ ΡΠ΅ΡΠ΅Π½Π·ΠΈΡΠ΅ Π½ΠΈΡΡ Π²Π΅ΡΠΈΡΠΈΠΊΠΎΠ²Π°Π½Π΅ Β Π‘Π°Π·Π½Π°ΡΡΠ΅ Π²ΠΈΡΠ΅
Π ΠΎΠ²ΠΎΡ Π΅-ΠΊΡΠΈΠ·ΠΈ
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 ...
ΠΡΠ΅Π½ΠΈΡΠ΅ ΠΎΠ²Ρ Π΅-ΠΊΡΠΈΠ³Ρ
ΠΠ°Π²ΠΈΡΠ΅ Π½Π°ΠΌ ΡΠ²ΠΎΡΠ΅ ΠΌΠΈΡΡΠ΅ΡΠ΅.
ΠΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ΅ ΠΎ ΡΠΈΡΠ°ΡΡ
ΠΠ°ΠΌΠ΅ΡΠ½ΠΈ ΡΠ΅Π»Π΅ΡΠΎΠ½ΠΈ ΠΈ ΡΠ°Π±Π»Π΅ΡΠΈ
ΠΠ½ΡΡΠ°Π»ΠΈΡΠ°ΡΡΠ΅ Π°ΠΏΠ»ΠΈΠΊΠ°ΡΠΈΡΡ Google Play ΠΊΡΠΈΠ³Π΅ Π·Π° Android ΠΈ iPad/iPhone. ΠΡΡΠΎΠΌΠ°ΡΡΠΊΠΈ ΡΠ΅ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΡΡΠ΅ ΡΠ° Π½Π°Π»ΠΎΠ³ΠΎΠΌ ΠΈ ΠΎΠΌΠΎΠ³ΡΡΠ°Π²Π° Π²Π°ΠΌ Π΄Π° ΡΠΈΡΠ°ΡΠ΅ ΠΎΠ½Π»Π°ΡΠ½ ΠΈ ΠΎΡΠ»Π°ΡΠ½ Π³Π΄Π΅ Π³ΠΎΠ΄ Π΄Π° ΡΠ΅ Π½Π°Π»Π°Π·ΠΈΡΠ΅.
ΠΠ°ΠΏΡΠΎΠΏΠΎΠ²ΠΈ ΠΈ ΡΠ°ΡΡΠ½Π°ΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π°ΡΠ΄ΠΈΠΎ-ΠΊΡΠΈΠ³Π΅ ΠΊΡΠΏΡΠ΅Π½Π΅ Π½Π° Google Play-Ρ ΠΏΠΎΠΌΠΎΡΡ Π²Π΅Π±-ΠΏΡΠ΅Π³Π»Π΅Π΄Π°ΡΠ° Π½Π° ΡΠ°ΡΡΠ½Π°ΡΡ.
Π-ΡΠΈΡΠ°ΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΠ΅ΡΠ°ΡΠΈ
ΠΠ° Π±ΠΈΡΡΠ΅ ΡΠΈΡΠ°Π»ΠΈ Π½Π° ΡΡΠ΅ΡΠ°ΡΠΈΠΌΠ° ΠΊΠΎΡΠ΅ ΠΊΠΎΡΠΈΡΡΠ΅ Π΅-ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΠΎ ΡΡΠΎ ΡΡ Kobo Π΅-ΡΠΈΡΠ°ΡΠΈ, ΡΡΠ΅Π±Π° Π΄Π° ΠΏΡΠ΅ΡΠ·ΠΌΠ΅ΡΠ΅ ΡΠ°ΡΠ» ΠΈ ΠΏΡΠ΅Π½Π΅ΡΠ΅ΡΠ΅ Π³Π° Π½Π° ΡΡΠ΅ΡΠ°Ρ. ΠΡΠ°ΡΠΈΡΠ΅ Π΄Π΅ΡΠ°ΡΠ½Π° ΡΠΏΡΡΡΡΠ²Π° ΠΈΠ· ΡΠ΅Π½ΡΡΠ° Π·Π° ΠΏΠΎΠΌΠΎΡ Π΄Π° Π±ΠΈΡΡΠ΅ ΠΏΡΠ΅Π½Π΅Π»ΠΈ ΡΠ°ΡΠ»ΠΎΠ²Π΅ Ρ ΠΏΠΎΠ΄ΡΠΆΠ°Π½Π΅ Π΅-ΡΠΈΡΠ°ΡΠ΅.
