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P. E. Alaev 《Siberian Advances in Mathematics》2008,18(4):227-241
We study countable Boolean algebras with finitely many distinguished ideals (countable I-algebras) whose elementary theory is countably categorical, and autostable I-algebras which form their subclass. We propose a new characterization for the former class that allows to answer a series of questions about the structure of countably categorical and autostable I-algebras. 相似文献
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P. E. Alaev 《Algebra and Logic》1999,38(6):353-366
We deal with problems associated with Scott ranks of Boolean algebras. The Scott rank can be treated as some measure of complexity
of an algebraic system. Our aim is to propound and justify the procedure which, given any countable Boolean algebra, will
allow us to construct a Boolean algebra of a small Scott rank that has the same natural algebraic complexity as has the initial
algebra. In particular, we show that the Scott rank does not always serve as a good measure of complexity for the class of
Boolean algebras. We also study into the question as to whether or not a Boolean algebra of a big Scott rank can be decomposed
into direct summands with intermediate ranks. Examples are furnished in which Boolean algebras have an arbitrarily big Scott
rank such that direct summands in them either have a same rank or a fixed small one, and summands of intermediate ranks are
altogether missing. This series of examples indicates, in particular, that there may be no nontrivial mutual evaluations for
the Scott and Frechet ranks on a class of countable Boolean algebras.
Supported by RFFR grant No. 99-01-00485, by a grant for Young Scientists from SO RAN, 1997, and by the Federal Research Program
(FRP) “Integration”.
Translated fromAlgebra i Logika, Vol. 38, No. 6, pp. 643–666, November–December, 1999. 相似文献
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Computable Homogeneous Boolean Algebras and a Metatheorem 总被引:1,自引:0,他引:1
P. E. Alaev 《Algebra and Logic》2004,43(2):73-87
We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of
-computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras. 相似文献
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We prove a general theorem that allows us to pass from a hyperarithmetical Boolean algebra with a distinguished ideal to some computable Boolean algebra connected with the former by natural algebraic operations. Some examples are given. 相似文献
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V. V. Korshak V. A. Sergeev Yu. A. Chernomordik S. B. Alaev 《Russian Chemical Bulletin》1977,26(7):1515-1517
Conclusions Some oligophenylenes were synthesized from biacetylene and aliphatic monoacetylenic compounds. Their structure and some of the properties of film coatings obtained from them were studied.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1645–1648, July, 1977. 相似文献