Titlebook: Studies in Constructive Mathematics and Mathematical Logic; Part I A. O. Slisenko Book 1969 Consultants Bureau 1969 Calc.Logic.Mint.Volume.

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Variation in the Deduction Search Tactics in Sequential Calculi,re constructed by the usual method from free variables by utilizing functional symbols. Expressions which may be obtained from terms (formulas) by replacing some number (possibly zero) of entries of free variables by entries of bound variables, will be called quasi-terms (or quasi- formulas).

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On the Correction of Unprovable Formulas,n the propositional and predicate calculuses. The question of machine programs capable of generating “sufficiently interesting” theorems of some kind of axiomatically given theories is also discussed in the literature. The difficulty in this problem is the question of what theorems might naturally b

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Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols,f a finite proof of the possibility of extending the fundamental theorem to predicate calculus with equality and functional symbols is proposed herein. In the course of the proof we shall establish several theorems on specialization of the form of the deduction in some sequential versions of the pre

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Invertible Sequential Variant of Constructive Predicate Calculus,lary formula property” is satisfied, possess enormous advantages. The invertible calculuses, i.e., those for which the sequent-conclusion is de-ducible for any rule of deduction if and only if the sequent-premises are deducible, are particularly advantageous. In attempting a deduction search in such

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