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1.
A. I. Stukachev 《Algebra and Logic》2007,46(6):419-432
Presentations of structures in admissible sets, as well as different relations of effective reducibility between the structures,
are treated. Semilattices of degrees of Σ-definability are the main object of investigation. It is shown that the semilattice
of degrees of Σ-definability of countable structures agrees well with semilattices of T-and e-degrees of subsets of natural
numbers. Also an attempt is made to study properties of the structures that are inherited under various effective reducibilities
and explore how degrees of presentability depend on choices of different admissible sets as domains for presentations.
Supported by RFBR grant Nos. 05-0100481 and 06-0104002, by the Council for Grants (under RF President) for State Support of
Young Candidates of Science and Their Supervisors via project MK-1239.2005.1, and via INTAS project YSF 04-83-3310.
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Translated from Algebra i Logika, Vol. 46, No. 6, pp. 763–788, November–December, 2007. 相似文献
2.
V. M. Murzina 《Algebra and Logic》2007,46(6):409-418
We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007. 相似文献
3.
It is proved that the exponential growth rate of identities in any superalgebra with a nilpotent commutator subalgebra over
a field of zero characteristic is an integer.
Supported by RFBR (project Nos. 07-01-00080 and 06-01-00485) and by the Council for Grants (under RF President) and State
Aid of Leading Scientific Schools (grant NSh-1983.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 617–645, September–October, 2008. 相似文献
4.
A. N. Koryukin 《Algebra and Logic》2005,44(2):73-81
We estimate Gröbner-Shirshov bases for the Lie algebra An given arbitrary orders of generators (nodes of a Dynkin graph). Previously, the Gröbner-Shirshov basis was computed in [1] for the particular case where nodes of the Dynkin graph are ordered successively.Supported by RFBR grant Nos. 05-01-00230 and 02-01-00258 and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 131–147, March–April, 2005. 相似文献
5.
6.
V. D. Mazurov 《Algebra and Logic》2005,44(1):31-39
It is proved that a group G generated by a conjugacy class X of elements of order 3, so that every two non-commuting elements of X generate a subgroup isomorphic to an alternating group of degree 4 or 5, is locally finite. More precisely, either G contains a normal elementary 2-subgroup of index 3, or G is isomorphic to an alternating group of permutations on some (possibly infinite) set.Supported by RFBR grant Nos. 02-01-00495 and 02-01-39005, by FP Universities of Russia grant No. UR.04.01.0202, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 54–69, January–February, 2005. 相似文献
7.
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime
graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set
with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders
on these sets; the information obtained is collected in tables. We consider several applications of these results to various
problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1; by the RF Ministry of Education Developmental Program for Scientific Potential of the Higher
School of Learning, project No. 8294; by FP “Universities of Russia,” grant No. UR.04.01.202; and by Presidium SB RAS grant
No. 86-197.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 682–725, November–December, 2005. 相似文献
8.
O. V. Zeevald 《Algebra and Logic》2006,45(6):415-430
We explore the basic fuzzy logic BL as well as propositional fuzzy logics with modalities □ and ◊ and a total accessibility relation. Formulations and proofs
are given to replacement theorems for BL. A basic calculus of modal fuzzy logic is introduced. For this calculus and its extensions, we prove replacement and deduction
theorems.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 45, No. 6, pp. 731–757, November–December, 2006. 相似文献
9.
L. L. Maksimova 《Algebra and Logic》2005,44(6):407-421
We study into the interpolation property and the projective Beth property in extensions of Johansson's minimal logic. A family
of logics of some special form is considered. Effective criteria are specified which allow us to verify whether an arbitrary
logic in this family has a given property.
Supported by RFBR grant No. 03-06-80178, by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1, and by INTAS grant No. 04-77-7080.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 726–750, November–December, 2005. 相似文献
10.
S. V. Sudoplatov 《Algebra and Logic》2007,46(2):134-146
A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition
of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous
model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions
to be saturated.
Supported by RFBR grant No. 05-01-00411, and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools via project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 2, pp. 244–268, March–April, 2007. 相似文献
11.
M. V. Semenova 《Algebra and Logic》2005,44(4):270-285
Various types of lattices are embedded in suborder lattices of posets possessing certain properties. In particular, it is shown that the class of lattices isomorphic to sublattices of suborder lattices of posets of length at most n is a variety, for any n < ω.Supported by INTAS-YSF grant 2001/1-65, by RFBR-DFG grant No. 01-01-04003, by RF Ministry of Education grant No. E02-1.0-32, by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2112.2003.1, and by a grant from the Russian Science Support Foundation.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 483–511, July–August, 2005. 相似文献
12.
Spectra of finite linear and unitary groups 总被引:1,自引:0,他引:1
A. A. Buturlakin 《Algebra and Logic》2008,47(2):91-99
The spectrum of a finite group is the set of its element orders. An arithmetic criterion determining whether a given natural
number belongs to a spectrum of a given group is furnished for all finite special, projective general, and projective special
linear and unitary groups.
Supported by RFBR (grant Nos. 08-01-00322 and 06-01-39001) and by the Council for Grants (under RF President) and State Aid
of Leading Scientific Schools (project NSh-344.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 157–173, March–April, 2008. 相似文献
13.
L. L. Maksimova 《Algebra and Logic》2009,48(1):33-53
The restricted interpolation property IPR in modal and superintuitionistic logics is investigated. It is proved that in superintuitionistic
logics of finite slices and in finite-slice extensions of the Grzegorczyk logic, the property IPR is equivalent to the projective
Beth property PB2.
Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific
Schools (grant NSh-335.2008.1).
Translated from Algebra i Logika, Vol. 48, No. 1, pp. 54-89, January-February, 2009. 相似文献
14.
E. A. Palyutin 《Algebra and Logic》2005,44(5):326-335
A question is studied as to which properties (classes) of elementary theories can be defined via generalized stability. We
present a topological account of such classes. It is stated that some well-known classes of theories, such as strongly minimal,
o-minimal, simple, etc., are stably definable, whereas, for instance, countably categorical, almost strongly minimal, ω-stable
ones, are not.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 583–600, September–October, 2005.
Supported by RFBR grant Nos. 02-01-00540 and 05-01-00411, and by the Council for Grants (under RF President) and State Aid
of Fundamental Science Schools, project NSh-2069.2003.1. 相似文献
15.
V. F. Murzina 《Algebra and Logic》2008,47(6):405-419
Using the language of temporal logic, we construct a decidable calculus L* α and prove that the calculus is complete w.r.t.
the class of all strictly linearly ordered α-frames.
Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific
Schools (grant NSh-335.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 6, pp. 723–749, November–December, 2008. 相似文献
16.
L. L. Maksimova 《Algebra and Logic》2007,46(5):341-353
The interpolation property in extensions of Johansson’s minimal logic is investigated. The construction of a matched product
of models is proposed, which allows us to prove the interpolation property in a number of known extensions of the minimal
logic. It is shown that, unlike superintuitionistic, positive, and negative logics, a sum of J-logics with the interpolation property CIP may fail to possess CIP, nor even the restricted interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 627–648, September–October, 2007. 相似文献
17.
A. V. Karpenko 《Algebra and Logic》2008,47(6):395-404
Conditions are specified which are necessary and sufficient for a logic over K4 to possess the weak interpolation property.
For this goal to be met, simple transitive modal algebras are described, and we establish a criterion for the class of such
algebras to be amalgamable. For extensions of K4, the weak interpolation property is proved decidable.
Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific
Schools (grant NSh-335.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 6, pp. 705–722, November–December, 2008. 相似文献
18.
A. I. Stukachev 《Algebra and Logic》2008,47(1):65-74
We show that the property of being locally constructivizable is inherited under Muchnik reducibility, which is weakest among
the effective reducibilities considered over countable structures. It is stated that local constructivizability of level higher
than 1 is inherited under Σ-reducibility but is not inherited under Medvedev reducibility. An example of a structure
and a relation P ⊆ M is constructed for which
but
≢∑
. Also, we point out a class of structures which are effectively defined by a family of their local theories.
Supported by RFBR (grant Nos. 05-0100481 and 06-0104002), by the Council for Grants (under RF President) for State Support
of Young Candidates of Science and Their Supervisors (project MK-1239.2005.1), and by INTAS (project YSF 04-83-3310).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 108–126, January–February, 2008. 相似文献
19.
We describe Novikov-Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative
derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of
characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established
between Novikov-Poisson algebras and Jordan superalgebras.
Supported by RFBR (grant No. 05-01-00230), by SB RAS (Integration project No. 1.9), and by the Council for Grants (under RF
President) and State Aid of Leading Scientific Schools (project NSh-344.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 186–202, March–April, 2008. 相似文献
20.
L. L. Maksimova 《Algebra and Logic》2006,45(1):49-66
We look at the interplay between the projective Beth property in non-classical logics and interpolation. Previously, we proved
that in positive logics as well as in superintuitionistic and modal ones, the projective Beth property PB2 follows from Craig's interpolation property and implies the restricted interpolation property IPR. Here, we show that IPR and PB2 are equivalent in positive logics, and also in extensions of the superintuitionistic logic KC and of the modal logic Grz.2.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 85–113, January–February, 2006. 相似文献