Studies in Constructive Mathematics and Mathematical Logic: Part I

Front Matter....Pages i-viii
Method of Establishing Deducibility in Classical Predicate Calculus....Pages 1-4
On the Correction of Unprovable Formulas....Pages 5-8
Lebesgue Integral in Constructive Analysis....Pages 9-14
Sufficient Conditions of Incompleteness for the Formalization of Parts of Arithmetic....Pages 15-20
Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols....Pages 21-23
Some Reduction Classes and Undecidable Theories....Pages 24-25
Deductive Validity and Reduction Classes....Pages 26-28
Problem of Decidability for Some Constructive Theories of Equalities....Pages 29-31
On Constructive Groups....Pages 32-35
Invertible Sequential Variant of Constructive Predicate Calculus....Pages 36-42
Choice of Terms in Quantifier Rules of Constructive Predicate Calculus....Pages 43-46
Analog of Herbrand’s Theorem for Prenex Formulas of Constructive Predicate Calculus....Pages 47-51
Variation in the Deduction Search Tactics in Sequential Calculi....Pages 52-59
Imbedding Operations Associated with Kripke’s “Semantics”....Pages 60-63
On Imbedding Operators....Pages 64-66
Undecidability of a Class of Formulas Containing Just One Single-Place Predicate Variable in Modal Calculus....Pages 67-69
Sequential Modification of Constructive Logic Calculus for Normal Formulas without Structural Deduction Rules....Pages 70-76
On Sequential Modifications of Applied Predicate Calculi....Pages 77-81
On Maximal Continuity Regulators for Constructive Functions....Pages 82-84
On the Representability of Algorithmically Decidable Predicates by Rabin Machines....Pages 85-88