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April-June, 2000

Volume 2, Issue 2

Issue is dedicated to 60th anniversary of the academician Yurii Leonidovich Ershov

Yurii Leonidovich Ershov. 60th Anniversary
S. S. Goncharov, I. A. Lavrov, V. D. Mazurov, A. A. Maltsev, A. S. Morozov, A. A. Nikitin, E. A. Palutin, D. M. Smirnov (Nobosibirsk)

Yurii Leonidovich Ershov

Article (rus.) - [pdf] [zip-pdf]

On a Sufficient Condition of Strong Constructivizability of Atomic Boolean Algebras
V. D. Dzgoev (Vladikavkaz)
UDC 510.6

The work deals with the proof of strong constructivizability of quotient algebra of constructive Boolean algebra by an ideal provided that numbers of the ideal compize a good set in ariphmetic hierarchy. The result was reported by the author at the IV All-Union confernce on mathemetical logic held in Kishinev in 1976 and was announced in [1]. Though complete proof had not been yet published.

Article (rus.) - [pdf] [zip-pdf]

On Frobenius Groups Containing an Element of Order 3
A. Kh. Zhurtov (Nalchik)
UDC 512.54

It is proved that Frobenius group G generated by two elements of order 3 is finite. The kernel of group G is abelian and the number of generators is not more than 8; the supplement is or cyclyc or isomorphic to one of the group SL2(3), SL2(5)
Article (rus.) - [pdf] [zip-pdf]

Unsolved Nonstandard Problems
A. G. Kusraev (Vladikavkaz), S. S. Kutateladze (Novosibirsk)
UDC 517.98

In the fall of 1990 we arranged a small colloquium on nonstandard analysis at the request of a group of graduate and postgraduate students of Novosibirsk State University. E.I. Gordon and A.G. Kachurovski also took part in discussions. At the meetings many unsolved problems were formulated stemming from various branches of analysis and seemingly deserving attention of the novices of nonstandard analysis. The list of problems was written in the article.

In 1994 some discussion took place on combining nonstandard methods at the international conference "Interaction Between Functional Analysis, Harmonic Analysis and Probability" (Missouri University, Columbia USA). The same topics were submitted to the international conference "Analysis and Logic" held in Belgium in 1997.

In 1998 an INTAS research project was submitted with the participation of A. Wickstead, E. I. Gordon, M. Wolff , A. G. Kusraev, and S. S. Kutateladze. The problems raised in the framework of these projects are the core of this article. The list of the problems contains not only simple questions for drill but also topics for serious research intended mostly at the graduate and post graduate level. Some problems need creative thought to clarify and specify them.

Article (eng.) - [pdf] [zip-pdf]

About Projective Planes Over Weak-Distributive Bodies and IPOVW-Systems
I. A. Khubezhty (Vladikavkaz)UDC {512.552.32+514.146.7}

Article (rus.) - [pdf] [zip-pdf]




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