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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A. O. Slisenkof numerical cognition. The volume then moves to discussing various aspects of mathematics education, including Charles Davies’s early book on the teaching of mathematics and the use of Gaussian Lemniscates in the classroom. A collection of papers on the history of mathematics in the nineteenth centu

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temperate

LEERY

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Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols,dicate calculus with equality and functional symbols which are free of sections. In themselves, these results turn out to be useful for the proof of a number of assertions connected with the predicate calculus with equality and functional symbols.

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On Imbedding Operators,m S. then the imbedding operator φ from S. into S. is called regular (see [1]) if for any formula A of the system S. the formula A ⊃ φ(A) is deducible in S. (when all the formulas deducible in S. are true in a certain interpretation, there results from the regularity of the imbedding operator that it transforms a true formula into a true formula).

APRON

Sequential Modification of Constructive Logic Calculus for Normal Formulas without Structural Deduc calculus NK. was introduced and investigated by A. V. Idel’son in [3]. A. V. Idel’son reduced the question of a foundation for the calculus NK. to the foundation for a considerably simpler calculus NN. in whose language only normal formulas without subordinate variables can be constructed (Theorem 12.3.1 from [3]).

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On the Correction of Unprovable Formulas,of axiomatically given theories is also discussed in the literature. The difficulty in this problem is the question of what theorems might naturally be considered “sufficiently interesting.” Some possible approaches to this theorem are considered in [1], [2], [3].

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,Analog of Herbrand’s Theorem for Prenex Formulas of Constructive Predicate Calculus,-free formulas whose structure recalls the structure of the Herbrand developments [1] of the formula A. The concepts introduced in [2], which are connected with k-systems of Skolem functions and k-lexicons of formulas, will be utilized.