Zap. Nauchn. Sem. LOMI, 1968, Volume 8

JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

1968, Volume 8

Contents

Studies in constructive mathematics and mathematical logic. Part II

	Preface A. O. Slisenko		7
	Some notes on proof searching in predicate calculus G. V. Davydov		8
	Lebesgue integral and the notion of measurability of functions in constructive analysis O. Demuth		21
	A connection between Riemann and Lebesgue integrability of constructive functions O. Demuth		29
	A computability of primitive recursive terms of finite type and the primitive recursive realization A. G. Dragalin		32
	Word operator algorithms A. G. Dragalin		46
	A constructive classification of arithmetical predicates and semantical bases for arithmetic M. M. Kipnis		53
	On a system of operators, simplifying the combination theory of $K$-algorithms N. K. Kossovski		66
	A construction of basic operators of the combination theory of $K$-algorithms, using operators of a simple kind N. K. Kossovski		80
	Some examples of quasidense, but not dense sets of duplexes B. A. Kushner		95
	A note on domains of constructive functions B. A. Kushner		103
	Some properties of $F$-numbers B. A. Kushner, G. S. Tseitin		107
	On constructive analytical functions of one real variable V. A. Lifshits		121
	A connection between systems of words-and-lengths equations and Hilbert's tenth problem Yu. V. Matiyasevich		132
	Two reductions of Hilbert's tenth problem Yu. V. Matiyasevich		145
	Arithmetical representations of powers Yu. V. Matiyasevich		159
	Cut-free calculi of the $S5$-type G. E. Mints		166
	The implicative complexity of axiomatics G. E. Mints		175
	A disjunctive interpretation of the $LJ$ calculus G. E. Mints		182
	Permissible and derivable rules G. E. Mints		189
	The independence of postulates of natural calculi G. E. Mints		192
	Glivenko classes of sequents V. P. Orevkov		196
	Two unsolvable classes of formulas of classical predicate calculus V. P. Orevkov		202
	Kanger's variant of predicate calculus with not totally defined functions R. A. Plyushkevitchus		211
	A complexity characteristic of recursive predicates, which does not depend on standardization of the notion of algorithm R. I. Freidson		225
	On the complexity of proof in prepositional calculus G. S. Tseitin		234
	On the disjunctive rank of formulas of constructive arithmetic G. S. Tseitin		260
	Total constructive sets with equalities and some their properties V. A. Shurygin		272