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1.
Barbara Majcher‐Iwanow 《Mathematical Logic Quarterly》2008,54(6):597-616
Let G be a closed subgroup of S∞ and X be a Polish G ‐space. To every x ∈ X we associate an admissible set A x and show how questions about X which involve Baire category can be formalized in A x . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
A. N. Khisamiev 《Siberian Mathematical Journal》2006,47(3):574-583
We obtain conditions for the Σ-definability of a subset of the set of naturals in the hereditarily finite admissible set over a model and for the computability of a family of such subsets. We prove that: for each e-ideal I there exists a torsion-free abelian group A such that the family of e-degrees of Σ-subsets of ω in $\mathbb{H}\mathbb{F}(A)$ coincides with I; there exists a completely reducible torsion-free abelian group in the hereditarily finite admissible set over which there exists no universal Σ-function; for each principal e-ideal I there exists a periodic abelian group A such that the family of e-degrees of Σ-subsets of ω in $\mathbb{H}\mathbb{F}(A)$ coincides with I. 相似文献
3.
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
4.
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.
__________
Translated from Algebra i Logika, Vol. 46, No. 6, pp. 763–788, November–December, 2007. 相似文献
5.
Characterizations of γ-open sets and locally γ-regular sets are given. We generalize some already established results and answer an open question by giving a characterization
to γ-quasi-open sets.
相似文献
6.
We find some links between -reducibility and T-reducibility. We prove that (1) if a quasirigid model is strongly -definable in a hereditarily finite admissible set over a locally constructivizable B-system, then it is constructivizable; (2) every abelian p-group and every Ershov algebra is locally constructivizable; (3) if an antisymmetric connected model is -definable in a hereditarily finite admissible set over a countable Ershov algebra then it is constructivizable. 相似文献
7.
It is shown that the class of all possible families of -subsets of finite ordinals in admissible sets coincides with a class of all non-empty families closed under e-reducibility and . The construction presented has the property of being minimal under effective definability. Also, we describe the smallest (w.r.t. inclusion) classes of families of subsets of natural numbers, computable in hereditarily finite superstructures. A new series of examples is constructed in which admissible sets lack in universal -function. Furthermore, we show that some principles of classical computability theory (such as the existence of an infinite non-trivial enumerable subset, existence of an infinite computable subset, reduction principle, uniformization principle) are always satisfied for the classes of all -subsets of finite ordinals in admissible sets. 相似文献