共查询到20条相似文献,搜索用时 312 毫秒
1.
Andrés Eduardo Caicedo Paul Larson Grigor Sargsyan Ralf Schindler John Steel Martin Zeman 《Israel Journal of Mathematics》2017,217(1):231-261
By forcing with Pmax over strong models of determinacy, we obtain models where different square principles at ω 2 and ω 3 fail. In particular, we obtain a model of \({2^{{\aleph _0}}} = {2^{{\aleph _1}}} = {\aleph _2} + {\neg }\square \left( {{\omega _2}} \right) + {\neg }\square \left( {{\omega _3}} \right)\). 相似文献
2.
The cardinal invariant Noetherian type Nt(X) of a topological space X was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2:
- There are spaces X and Y such that Nt(X×Y)< min{Nt(X), Nt(Y)}.
- In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace.
3.
Maryam Salimi Sean Sather-Wagstaff Elham Tavasoli Siamak Yassemi 《Algebras and Representation Theory》2014,17(1):103-120
Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an isomorphism $\operatorname{Tor}^{{\mathcal{F}_C}\mathcal{M}}_{i}(-,-) \cong \operatorname{Tor}^{{\mathcal{P}_C}\mathcal{M}}_{i}(-,-)$ between the bifunctors defined via C-flat and C-projective resolutions. We show how the vanishing of these functors characterizes the finiteness of ${{\mathcal{F}_C}\text{-}\operatorname{pd}}$ , and use this to give a relation between the ${{\mathcal{F}_C}\text{-}\operatorname{pd}}$ of a module and of a pure submodule. On the other hand, we show that other isomorphisms force C to be trivial. 相似文献
4.
We study some properties of the quotient forcing notions ${Q_{tr(I)} = \wp(2^{< \omega})/tr(I)}$ and P I ?= B(2 ω )/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2 ω . We show that the remainder forcing R I =?Q tr(I)/P I is σ-closed in these cases. We also study the cardinal invariant of the continuum ${\mathfrak{h}_{\mathbb{Q}}}$ , the distributivity number of the quotient ${Dense(\mathbb{Q})/nwd}$ , in order to show that ${\wp(\mathbb{Q})/nwd}$ collapses ${\mathfrak{c}}$ to ${\mathfrak{h}_{\mathbb{Q}}}$ , thus answering a question addressed in Balcar et?al. (Fundamenta Mathematicae 183:59–80, 2004). 相似文献
5.
Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. 相似文献
6.
Andrey S. Trepalin 《Central European Journal of Mathematics》2014,12(2):229-239
Let $\Bbbk$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $\Bbbk$ . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $\Bbbk$ is algebraically closed. In this paper we prove that ${{\mathbb{P}_\Bbbk ^2 } \mathord{\left/ {\vphantom {{\mathbb{P}_\Bbbk ^2 } G}} \right. \kern-0em} G}$ is rational for an arbitrary field $\Bbbk$ of characteristic zero. 相似文献
7.
A. P. Oskolkov 《Journal of Mathematical Sciences》1978,10(1):95-103
For the system of Navier-Stokes-Voigt equations $$\frac{{\partial \vec v}}{{\partial t}} - v\Delta \vec v - \aleph \frac{{\partial \Delta \vec v}}{{\partial t}} + v_\kappa \frac{{\partial \Delta \vec v}}{{\partial x_\kappa }} + grad \rho = 0, div \vec v = 0$$ and the BBM equation $$\frac{{\partial v}}{{\partial t}} + v\frac{{\partial \Delta v}}{{\partial x}} - \frac{{\partial ^3 v}}{{\partial t\partial x^2 }} = 0$$ characteristic functions \(\mathcal{F}\left( {\vec \theta ;t} \right)\) of the measure μt(ω)=μ(V ?1 t (ω)), describing the evolution in time of the probability measure μ(ω) defined on the set of initial conditions for the first initial boundary-value problem for system (1) or Eq. (2) are constructed and investigated. It is shown that the characteristic functions \(\mathcal{F}\left( {\vec \theta ;t} \right)\) constructed satisfy partial differential equations with an infinite number of independent variables (t; θ1,θ2,...) [the statistical equations of E. Hopf for the system (1) or Eq. (2)]. 相似文献
8.
There are several examples in the literature showing that compactness-like properties of a cardinal κ cause poor behavior of some generic ultrapowers which have critical point κ (Burke [1] when κ is a supercompact cardinal; Foreman-Magidor [6] when κ = ω 2 in the presence of strong forcing axioms). We prove more instances of this phenomenon. First, the Reflection Principle (RP) implies that if $\overrightarrow I $ is a tower of ideals which concentrates on the class $GI{C_{{\omega _1}}}$ of ω 1-guessing, internally club sets, then $\overrightarrow I $ is not presaturated (a set is ω 1-guessing iff its transitive collapse has the ω 1-approximation property as defined in Hamkins [10]). This theorem, combined with work from [16], shows that if PFA + or MM holds and there is an inaccessible cardinal, then there is a tower with critical point ω 2 which is not presaturated; moreover, this tower is significantly different from the non-presaturated tower already known (by Foreman-Magidor [6]) to exist in all models of Martin’s Maximum. The conjunction of the Strong Reflection Principle (SRP) and the Tree Property at ω 2 has similar implications for towers of ideals which concentrate on the wider class $GI{C_{{\omega _1}}}$ of ω 1-guessing, internally stationary sets. Finally, we show that the word “presaturated” cannot be replaced by “precipitous” in the theorems above: Martin’s Maximum (which implies SRP and the Tree Property at ω 2) is consistent with a precipitous tower on $GI{C_{{\omega _1}}}$ . 相似文献
9.
Ahmet Çevik 《Archive for Mathematical Logic》2013,52(1-2):137-142
We prove two antibasis theorems for ${\Pi^0_1}$ classes. The first is a jump inversion theorem for ${\Pi^0_1}$ classes with respect to the global structure of the Turing degrees. For any ${P\subseteq 2^\omega}$ , define S(P), the degree spectrum of P, to be the set of all Turing degrees a such that there exists ${A \in P}$ of degree a. For any degree ${{\bf a \geq 0'}}$ , let ${\textrm{Jump}^{-1}({\bf a) = \{b : b' = a \}}}$ . We prove that, for any ${{\bf a \geq 0'}}$ and any ${\Pi^0_1}$ class P, if ${\textrm{Jump}^{-1} ({\bf a}) \subseteq S(P)}$ then P contains a member of every degree. For any degree ${{\bf a \geq 0'}}$ such that a is recursively enumerable (r.e.) in 0', let ${Jump_{\bf \leq 0'} ^{-1}({\bf a)=\{b : b \leq 0' \textrm{and} b' = a \}}}$ . The second theorem concerns the degrees below 0'. We prove that for any ${{\bf a\geq 0'}}$ which is recursively enumerable in 0' and any ${\Pi^0_1}$ class P, if ${\textrm{Jump}_{\bf \leq 0'} ^{-1}({\bf a)} \subseteq S(P)}$ then P contains a member of every degree. 相似文献
10.
A Gizatullin surface is a normal affine surface V over $ \mathbb{C} $ , which can be completed by a zigzag; that is, by a linear chain of smooth rational curves. In this paper we deal with the question of uniqueness of $ \mathbb{C}^{ * } $ -actions and $ \mathbb{A}^{{\text{1}}} $ -fibrations on such a surface V up to automorphisms. The latter fibrations are in one to one correspondence with $ \mathbb{C}_{{\text{ + }}} $ -actions on V considered up to a “speed change”. Non-Gizatullin surfaces are known to admit at most one $ \mathbb{A}^{1} $ -fibration V → S up to an isomorphism of the base S. Moreover, an effective $ \mathbb{C}^{ * } $ -action on them, if it does exist, is unique up to conjugation and inversion t $ \mapsto $ t ?1 of $ \mathbb{C}^{ * } $ . Obviously, uniqueness of $ \mathbb{C}^{ * } $ -actions fails for affine toric surfaces. There is a further interesting family of nontoric Gizatullin surfaces, called the Danilov-Gizatullin surfaces, where there are in general several conjugacy classes of $ \mathbb{C}^{ * } $ -actions and $ \mathbb{A}^{{\text{1}}} $ -fibrations, see, e.g., [FKZ1]. In the present paper we obtain a criterion as to when $ \mathbb{A}^{{\text{1}}} $ -fibrations of Gizatullin surfaces are conjugate up to an automorphism of V and the base $ S \cong \mathbb{A}^{{\text{1}}} $ . We exhibit as well large subclasses of Gizatullin $ \mathbb{C}^{ * } $ -surfaces for which a $ \mathbb{C}^{ * } $ -action is essentially unique and for which there are at most two conjugacy classes of $ \mathbb{A}^{{\text{1}}} $ -fibrations over $ \mathbb{A}^{{\text{1}}} $ . 相似文献
11.
Л. А. Шерстнева 《Analysis Mathematica》1988,14(4):323-345
Quasi-normed Lorentz spaces Λψ, q of 2π-periodic functions with quasinorms $$\left\| f \right\|_{\psi ,q} = \left\{ {\int\limits_0^{2\pi } {\psi ^q (t)\left[ {\frac{1}{t}\int\limits_0^t {f * (x)} dx} \right]} ^q \frac{{dt}}{t}} \right\}^{{1 \mathord{\left/ {\vphantom {1 q}} \right. \kern-\nulldelimiterspace} q}} $$ (0<q<∞,ω(t): [0,2π]→R is a continuous concave function with finite derivative everywhere on (0, 2gp)) and classes of functions $$H_{\psi ,q}^\omega \equiv \{ f(x):f(x) \in \Lambda _{\psi ,q} ;\mathop {\sup }\limits_{0 \leqq h \leqq \delta } \left\| {f(x + h) - f(x)} \right\|_{\psi ,q} = O\{ \omega (\delta )\} , \delta \to + 0\} $$ (ω(δ) — modulus of continuity) are studied. Precise embedding conditions of classes H ψ, q ω into Lorentz spaces and into each other are obtained: $$\begin{array}{*{20}c} {H_{\psi ,q_1 }^\omega \subset \Lambda _{\psi ,q_2 } ;} & {H_{\psi ,q_1 }^\omega \subset {\rm H}_{\psi ,q_2 }^{\omega * } ,} & {0< q_2< q_1< \infty ,} \\ \end{array} $$ under conditions \(\mathop {\lim }\limits_{t \to \infty } \frac{{\psi (2t)}}{{\psi (t)}} > 1,\mathop {\overline {\lim } }\limits_{x \to \infty } \frac{{\psi (2t)}}{{\psi (t)}}< 2\) andω(δ)=O{ω(δ 2)},δ→+0, andω * (δ) is an arbitrary modulus of continuity. 相似文献
12.
Zhao Xishun 《数学学报(英文版)》1990,6(1):42-46
In this paper, we prove that ifZFC is consistent, then so are the following theories: $$\begin{gathered} ZFC + MA + KT(\omega _2 ) + 2^{\aleph _0 } = \aleph _2 , \hfill \\ ZFC + SOCA + KT(\omega _2 ), \hfill \\ ZFC + SOCA1 + KT(\omega _2 ), \hfill \\ ZFC + OCA + KT(\omega _2 ), \hfill \\ ZFC + ISA + KT(\omega _2 ), \hfill \\ \end{gathered} $$ whereMA denotes Martin's axiom.KT(ω 2) the statement:“There exists anω 2-Kurepa tree”, andSOCA, SOCA1,OCA andISA are axioms introduced in [1]. 相似文献
13.
Let A and H be two Hopf algebras. We shall classify up to an isomorphism that stabilizes A all Hopf algebras E that factorize through A and H by a cohomological type object ${\mathcal H}^{2} (A, H)$ . Equivalently, we classify up to a left A-linear Hopf algebra isomorphism, the set of all bicrossed products A???H associated to all possible matched pairs of Hopf algebras $(A, H, \triangleleft, \triangleright)$ that can be defined between A and H. In the construction of ${\mathcal H}^{2} (A, H)$ the key role is played by special elements of $CoZ^{1} (H, A) \times {\rm Aut}\,_{\rm CoAlg}^1 (H)$ , where CoZ 1 (H, A) is the group of unitary cocentral maps and ${\rm Aut}\,_{\rm CoAlg}^1 (H)$ is the group of unitary automorphisms of the coalgebra H. Among several applications and examples, all bicrossed products H 4???k[C n ] are described by generators and relations and classified: they are quantum groups at roots of unity H 4n, ω which are classified by pure arithmetic properties of the ring ? n . The Dirichlet’s theorem on primes is used to count the number of types of isomorphisms of this family of 4n-dimensional quantum groups. As a consequence of our approach the group Aut Hopf(H 4n, ω ) of Hopf algebra automorphisms is fully described. 相似文献
14.
Peter Schenzel 《Archiv der Mathematik》2014,102(1):25-33
Let I denote an ideal in a commutative Noetherian ring R. Let M be an R-module. The I-adic completion is defined by ${\hat{M}^I = \varprojlim{}_{\alpha} M/I^{\alpha}M}$ . Then M is called I-adic complete whenever the natural homomorphism ${M \to \hat{M}^I}$ is an isomorphism. Let M be I-separated, i.e. ${\cap_{\alpha} I^{\alpha}M = 0}$ . In the main result of the paper, it is shown that M is I-adic complete if and only if ${{\rm Ext}_R^1(F,M) = 0}$ for the flat test module ${F = \oplus_{i = 1}^r R_{x_i}}$ , where ${\{x_1,\ldots,x_r\}}$ is a system of elements such that ${{\rm Rad} I = {\rm Rad}\, \underline{{\it x}} R}$ . This result extends several known statements starting with Jensen’s result [9, Proposition 3] that a finitely generated R-module M over a local ring R is complete if and only if ${{\rm Ext}^1_R(F,M) = 0}$ for any flat R-module F. 相似文献
15.
Let G be a compact Lie group. Consider the variety ${{\rm Hom}({\mathbb Z}^{k},G)}$ of representations of ${{\mathbb Z}^k}$ into G. We can see this as a based space by taking as base point the trivial representation . The goal of this paper is to prove that ${\pi_1({\rm Hom}({\mathbb Z}^k,G))}$ is naturally isomorphic to π 1(G) k . 相似文献
16.
Miloš S. Kurilić 《Archive for Mathematical Logic》2013,52(7-8):793-808
17.
S. A. Lozhkin V. A. Konovodov 《Moscow University Computational Mathematics and Cybernetics》2012,36(2):81-91
Boolean formulae in a standard basis {&, ??, ?} with a specified alternation depth are analyzed. The alternation depth of the formula considered as a particular case of a circuit of functional elements is a if the maximum number of variations of the gates?? types on sequences, each being a path and not containing negations connected to the inputs is (a ? 1). The quantity L (a)(n) equal to the minimum complexity of a formula with an alternation depth no greater than a is introduced. It implements the function that is most complex in this sense. It was demonstrated by Lupanov that L (a)(n) is asymptotically equal to $\frac{{2^n }} {{\log _2 n}} $ at a ?? 3. This work reveals the behavior of this function for a ?? 3 at the level of high accuracy asymptotic bounds: $L^{(a)} (n) = \frac{{2^n }} {{\log _2 n}}\left( {1 + \frac{{\log _2^{[a - 1]} n \pm O(1)}} {{\log _2 n}}} \right), $ where $\log _2^{[a - 1]} n = \underbrace {\log _2 ...\log _2 n}_{(a - 1)times}$ with a relative error of $O\left( {\frac{1} {{\log n}}} \right) $ . 相似文献
18.
Piotr Zakrzewski 《Acta Mathematica Hungarica》2014,143(2):367-377
We study structural properties of the collection of all σ-ideals in the σ-algebra of Borel subsets of the Cantor group \(2^{\mathbb{N}}\) , especially those which satisfy the countable chain condition (ccc) and are translation invariant. We prove that the latter collection contains an uncountable family of pairwise orthogonal members and, as a consequence, a strictly decreasing sequence of length ω 1. We also make some observations related to the σ-ideal I ccc on \(2^{\mathbb{N}}\) , consisting of all Borel sets which belong to every translation invariant ccc σ-ideal on \(2^{\mathbb{N}}\) . In particular, improving earlier results of Rec?aw, Kraszewski and Komjáth, we show that:
- every subset of \(2^{\mathbb{N}}\) of cardinality less than can be covered by a set from I ccc,
- there exists a set C∈I ccc such that every countable subset Y of \(2^{\mathbb{N}}\) is contained in a translate of C.
19.
Wojciech Chojnacki 《Aequationes Mathematicae》2011,81(1-2):135-154
Let G be a commutative group, written additively, with a neutral element 0, and let K be a finite group. Suppose that K acts on G via group automorphisms ${G \ni a \mapsto ka \in G}$ , ${k \in K}$ . Let ${{\mathfrak{H}}}$ be a complex Hilbert space and let ${{\mathcal L}({\mathfrak{H}})}$ be the algebra of all bounded linear operators on ${{\mathfrak{H}}}$ . A mapping ${u \colon G \to {\mathcal L}({\mathfrak{H}})}$ is termed a K-spherical function if it satisfies (1) ${|K|^{-1} \sum_{k\in K} u (a+kb)=u (a) u (b)}$ for any ${a,b\in G}$ , where |K| denotes the cardinality of K, and (2) ${u (0) = {\rm id}_{\mathfrak {H}},}$ where ${{\rm id}_{\mathfrak {H}}}$ designates the identity operator on ${{\mathfrak{H}}}$ . The main result of the paper is that for each K-spherical function ${u \colon G \to {\mathcal {L}}({\mathfrak {H}})}$ such that ${\| u \|_{\infty} = \sup_{a\in G} \| u (a)\|_{{\mathcal L}({\mathfrak{H}})} < \infty,}$ there is an invertible operator S in ${{\mathcal L}({\mathfrak{H}})}$ with ${\| S \| \, \| S^{-1}\| \leq |K| \, \| u \|_{\infty}^2}$ such that the K-spherical function ${{\tilde{u}} \colon G \to {\mathcal L}({\mathfrak{H}})}$ defined by ${{\tilde{u}}(a) = S u (a) S^{-1},\,a \in G,}$ satisfies ${{\tilde{u}}(-a) = {\tilde{u}}(a)^*}$ for each ${a \in G}$ . It is shown that this last condition is equivalent to insisting that ${{\tilde{u}}(a)}$ be normal for each ${a \in G}$ . 相似文献
20.
Urs Hartl 《Inventiones Mathematicae》2013,193(3):627-696
In their book, Rapoport and Zink constructed rigid analytic period spaces ${\mathcal {F}}^{wa}$ for Fontaine’s filtered isocrystals, and period morphisms from PEL moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an étale bijective morphism ${\mathcal {F}}^{a}\to {\mathcal {F}}^{wa}$ of rigid analytic spaces and of a universal local system of ? p -vector spaces on ${\mathcal {F}}^{a}$ . Such a local system would give rise to a tower of étale covering spaces $\breve {{\mathcal {E}}}_{{\widetilde {K}}}$ of ${\mathcal {F}}^{a}$ , equipped with a Hecke-action, and an action of the automorphism group J(? p ) of the isocrystal with extra structure. For Hodge-Tate weights n?1 and n we construct in this article an intrinsic Berkovich open subspace ${\mathcal {F}}^{0}$ of ${\mathcal {F}}^{wa}$ and the universal local system on ${\mathcal {F}}^{0}$ . We show that only in exceptional cases ${\mathcal {F}}^{0}$ equals all of ${\mathcal {F}}^{wa}$ and when the Shimura group is $\operatorname {GL}_{n}$ we determine all these cases. We conjecture that the rigid-analytic space associated with ${\mathcal {F}}^{0}$ is the maximal possible ${\mathcal {F}}^{a}$ , and that ${\mathcal {F}}^{0}$ is connected. We give evidence for these conjectures. For those period spaces possessing PEL period morphisms, we show that ${\mathcal {F}}^{0}$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal p-divisible group and carries a J(? p )-linearization. We construct the tower $\breve {{\mathcal {E}}}_{{\widetilde {K}}}$ of étale covering spaces, and we show that it is canonically isomorphic in a Hecke and J(? p )-equivariant way to the tower constructed by Rapoport and Zink using the universal p-divisible group. 相似文献