共查询到20条相似文献,搜索用时 140 毫秒
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Given a computable ordinal Λ, the transfinite provability logic has for each a modality intended to represent a provability predicate within a chain of increasing strength. One possibility is to read as ? is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending .In this paper we will formalize such iterations of ω-rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that is sound and complete for any uniform provability predicate. 相似文献
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Giuseppe Baccella 《Journal of Algebra》2010,323(3):790-838
If R is a semiartinian von Neumann regular ring, then the set of primitive ideals of R, ordered by inclusion, is an artinian poset in which all maximal chains have a greatest element. Moreover, if has no infinite antichains, then the lattice of all ideals of R is anti-isomorphic to the lattice of all upper subsets of . Since the assignment defines a bijection from any set of representatives of simple right R-modules to , a natural partial order is induced in , under which the maximal elements are precisely those simple right R-modules which are finite dimensional over the respective endomorphism division rings; these are always R-injective. Given any artinian poset I with at least two elements and having a finite cofinal subset, a lower subset and a field D, we present a construction which produces a semiartinian and unit-regular D-algebra having the following features: (a) is order isomorphic to I; (b) the assignment realizes an anti-isomorphism from the lattice to the lattice of all upper subsets of ; (c) a non-maximal element of is injective if and only if it corresponds to an element of , thus is a right V-ring if and only if ; (d) is a right and left V-ring if and only if I is an antichain; (e) if I has finite dual Krull length, then is (right and left) hereditary; (f) if I is at most countable and , then is a countably dimensional D-algebra. 相似文献
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Let V be an orbit in of a finitely generated subgroup Λ of whose Zariski closure is suitably large (e.g. isomorphic to ). We develop a Brun combinatorial sieve for estimating the number of points on V for which a fixed set of integral polynomials take prime or almost prime values. A crucial role is played by the expansion property of the ‘congruence graphs’ that we associate with V. This expansion property is established when . To cite this article: J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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Nadia Hamida 《Comptes Rendus Mathematique》2006,342(11):807-812
For all , we define a p-adic regulator given by an explicit formula and we show that is non-trivial for . The main ideas come from a Note published in 2000 for the transcendental case. To cite this article: N. Hamida, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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In this paper we introduce a modal theory which is sound and complete for arithmetical -interpretations in , in other words, we will show that is the -provability logic of . Moreover we will show that is decidable. As a by-product of these results, we show that has de Jongh property. 相似文献
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Pooyan Moradifar Shahab Rajabi Siamak Yassemi 《Journal of Pure and Applied Algebra》2018,222(11):3757-3773
Given a non-unit, non-zero-divisor, central element x of a ring Λ, it is well known that many properties or invariants of Λ determine, and are determined by, those of and . In the present paper, we investigate how the property of “being tilting” behaves in this situation. It turns out that any tilting module over Λ gives rise to tilting modules over and after localization and passing to quotient respectively. On the other hand, it is proved that under some mild conditions, a module over Λ is tilting if its corresponding localization and quotient are tilting over and respectively. 相似文献
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Qiyu Sun 《Applied and Computational Harmonic Analysis》2012,32(3):329-341
In this paper, it is proved that every s-sparse vector can be exactly recovered from the measurement vector via some -minimization with , as soon as each s-sparse vector is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the -minimization can be so chosen to be about , where is the restricted isometry constant of order 2s for the measurement matrix A. 相似文献
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Erell Jamelot 《Comptes Rendus Mathematique》2004,339(11):809-814
An original approach of the singular complement method for Maxwell's equations in bounded polygonal domains is presented. A splitting of the electric field à la Moussaoui is proposed: , where , λ depends on the data and domain and is known explicitly. The same splitting can be used for the magnetic field. No cut-off function is needed and improved error estimates are derived. To cite this article: E. Jamelot, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
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Karl-Theodor Sturm 《Comptes Rendus Mathematique》2005,340(3):235-238
We introduce and analyze curvature bounds for metric measure spaces , based on convexity properties of the relative entropy . For Riemannian manifolds, if and only if for all . We define a complete separable metric on the family of all isomorphism classes of normalized metric measure spaces. It has a natural interpretation in terms of mass transportation. Our lower curvature bounds are stable under -convergence. We also prove that the family of normalized metric measure spaces with doubling constant is closed under -convergence. Moreover, the subfamily of spaces with diameter is compact. To cite this article: K.-T. Sturm, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献