Studies in Constructive Mathematics and Mathematical Logic: Part I

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.