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1.
The partial ordering of Medvedev reducibility restricted to the family of 01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a 01 class, which we call a ``c.e. separating class'. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.
Mathematics Subject Classification (2000): 03D30, 03D25 相似文献
2.
Studying computable representations of projective planes, for the classes K of pappian, desarguesian, and all projective planes, we prove that K c /? admits no hyperarithmetical Friedberg enumeration and admits a Friedberg Δ0α+3-computable enumeration up to a Δ0 α -computable isomorphism. 相似文献
3.
Linda Brown Westrick 《Israel Journal of Mathematics》2017,219(1):431-448
A family of sets is union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. Kleitman proved that every union-free family has size at most (1+o(1))( n/2 n ). Later, Burosch–Demetrovics–Katona–Kleitman–Sapozhenko asked for the number α(n) of such families, and they proved that \({2^{\left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)}} \leqslant \alpha \left( n \right) \leqslant {2^{2\sqrt 2 \left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)\left( {1 + o\left( 1 \right)} \right)}}\) They conjectured that the constant \(2\sqrt 2 \) can be removed in the exponent of the right-hand side. We prove their conjecture by formulating a new container-type theorem for rooted hypergraphs. 相似文献
4.
S. Yu. Podzorov 《Algebra and Logic》2005,44(2):82-94
We deal in specific features of the algebraic structure of Rogers semilattices of n
0-computable numberings, for n 2. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non 0-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.Supported by INTAS grant No. 00-499, by FP Universities of Russia grant UR.04.01.013, and by the Grant Center for Fundamental Research (GCFR), project PD02-1.1-475.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 148–172, March–April, 2005. 相似文献
5.
This paper is a sequel to our [7]. In that paper we constructed a 10 tree of avoidable points. Here we construct a 10 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2<. One interesting fact is that while our 10 tree of sharp filters (a subtree of <) is isomorphic to the tree of addresses (a subtree of 2<), the tree of addresses is recursively enumerable but not recursive. To achieve this end we use a finite injury priority argument.Mathematics Subject Classification (2000): 03D45, 03D80, 03C57, 54A20 相似文献
7.
Yemon Choi 《Semigroup Forum》2007,75(2):253-271
We show that if L is a semilattice then the ℓ1-convolution algebra of L is biflat precisely when L is "uniformly locally finite". Our proof technique shows in passing
that if this convolution algebra is biflat then it is isomorphic as a Banach algebra to the Banach space ℓ1(L) equipped with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous
characterisation of biflatness for Clifford semigroup algebras. 相似文献
8.
The prime graph of a finite group was introduced by Gruenberg and Kegel. The degree pattern of a finite group G associated to its prime graph was introduced in [1] and denoted by D(G). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions (1) |G| = |H| and (2) D(G) = D(H). Moreover, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Till now a lot of finite simple groups were shown to be OD-characterizable, and also some finite groups especially the automorphism
groups of some finite simple groups were shown not being OD-characterizable but k-fold OD-characterizable for some k > 1. In the present paper, the authors continue this topic and show that the automorphism groups of orthogonal groups O
10+(2) and O
10−(2) are OD-characterizable. 相似文献
9.
We point out that it is consistent with ZFC that 2
ω
> ℵ1 and every subset of ℝ is the ω
1 limit of a sequence of G
δ
sets in ℝ. We prove also that assuming cov (
) > ℵ1, not every set in ℝ is the ω
1 limit of a sequence of measurable sets. This solves two problems of T. Natkaniec and J. Wesołowska.
相似文献
10.
We use a distortion to define the dual complex of a cubical subdivision of ℝ
n
as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined
by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ
n
. 相似文献
11.
12.
For a fixed q ℕ and a given Σ1 definition φ(d,x), where d is a parameter, we construct a model M of 1 Δ0 + ? exp and a non standard d M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ(d,x) having no more than q alternations of blocks of quantifiers.
Received: 29 September 1998 / Revised version: 7 November 2001 Published online: 10 October 2002
RID="⋆"
ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13.
RID="⋆"
ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13. 相似文献
13.
Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty 10 subsets of 2, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w. We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M.Simpsons research was partially supported by NSF Grant DMS-0070718. We thank the anonymous referee for a careful reading of this paper and helpful comments. 相似文献
14.
Dimitra Kosta 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):102-109
Let X be a complete intersection of two hypersurfaces F
n
and F
k
in ℙ5 of degree n and k, respectively, with n ≥ k, such that the singularities of X are nodal and F
k
is smooth. We prove that if the threefold X has at most (n + k − 2)(n − 1) − 1 singular points, then it is factorial. 相似文献
15.
We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the
classes of continuous 2π-periodic functions whose (ψ, β)-derivatives belong to the set H
ω in the case where the sequences ψ that generate the classes tend to zero not faster than a power function. 相似文献
16.
M. A. Podkolzina 《Moscow University Mathematics Bulletin》2009,64(1):39-40
The problem on the number of precomplete classes in the functional system P κ τ is considered, elements of P κ τ are deterministic S-functions defined on words of length τ composed from letters of an alphabet of cardinality κ. An asymptotics for the number of S-precomplete classes in P κ τ is obtained for arbitrary fixed κ and τ tending to infinity. 相似文献
17.
We give necessary and sufficient conditions for the existence of pin± and spin structures on Riemannian manifolds with holonomy group 2k. For any n4 (resp. n6) we give examples of pairs of compact manifolds (resp. compact orientable manifolds) M1, M2, non homeomorphic to each other, that are Laplace isospectral on functions and on p-forms for any p and such that M1 admits a pin± (resp. spin) structure whereas M2 does not.Mathematics Subject Classification (2000):58J53, 57R15, 20H15Partially supported by Conicet and grants from SecytUNC, Foncyt and AgCba. 相似文献
18.
Stable rational cohomology groups of spaces of non-resultant homogeneous polynomial systems of growing degree in ?n are calculated. 相似文献
19.
S. P. Voitenko 《Ukrainian Mathematical Journal》2009,61(11):1728-1742
We obtain exact-order estimates for the best orthogonal trigonometric approximations of the classes B
Ω
p,θ of periodic functions of many variables in the space L
q
. 相似文献
20.
E. L. Shishkina 《Journal of Mathematical Sciences》2009,160(1):95-102
In [3], the inversion of an integral operator of potential type with constant characteristic generated by the many-dimensional
generalized shift was obtained. In this paper, the author obtains a generalization of the results from [3] to the case of a shift of mixed type, i.e., on a part of the variable generalized shifts of integral nature adopted to deal
with the Bessel singular differential operator act, whereas on the other part, the ordinary shift act. Also, it should be
noted that in contrast to [3], the integral of B-potential type with homogeneous characteristic is considered in this paper. This generalization is attained
by introducing general hypersingular integrals of the general form [8].
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献