Results 221 to 230 of about 5,027 (259)
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Journal of Symbolic Logic, 1998
Henson and Ross [1] answered the question of when two hyperfinite sets A, B in an ℵ1-saturated nonstandard universe are bijective by a Borel function: precisely when ∣A∣/∣B∣ ≈ 1. Živaljević [5] generalized this result to nonvanishing Borel sets. He defined a set to be nonvanishing if it is Loeb-measurable and has finite, non-zero measure with respect ...
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Henson and Ross [1] answered the question of when two hyperfinite sets A, B in an ℵ1-saturated nonstandard universe are bijective by a Borel function: precisely when ∣A∣/∣B∣ ≈ 1. Živaljević [5] generalized this result to nonvanishing Borel sets. He defined a set to be nonvanishing if it is Loeb-measurable and has finite, non-zero measure with respect ...
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Journal of Symbolic Logic, 1973
This paper is concerned with the hyderdegrees of elements of uncountable Borel subsets of ωω. The Borel subsets of ωω are the so-called Δ11 subsets of ωω, which are the subsets of ωω that are Δ11 in some parameter f: ω → ω.The results of this paper were inspired by two earlier results about the hyperdegrees of elements of Σ11 subsets of ωω.
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This paper is concerned with the hyderdegrees of elements of uncountable Borel subsets of ωω. The Borel subsets of ωω are the so-called Δ11 subsets of ωω, which are the subsets of ωω that are Δ11 in some parameter f: ω → ω.The results of this paper were inspired by two earlier results about the hyperdegrees of elements of Σ11 subsets of ωω.
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Borel sets and sectional matrices
Annals of Combinatorics, 1997Let \(I\) be a homogeneous ideal of the ring of polynomials \(k[x_1, x_2,\dots, x_n]\) over a field \(k\) of zero characteristic. The authors define the sectional matrix of \(I\) by its elements \[ M_I(i,d)= H_{(I+(L_1,L_2,\dots, L_{n-i}))/ (L_1, L_2,\dots, L_{n-i})} (d), \] where \(L_1, L_2,\dots, L_{n-i}\) are general linear forms and the expression ...
BIGATTI, ANNA MARIA, ROBBIANO, LORENZO
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CONFORMAL IMAGES OF BOREL SETS
Bulletin of the London Mathematical Society, 2003Let \(f\) be a function meromorphic on the unit disc \(D\) in the complex plane, and let \(C\) denote the unit circle. For a point \(\zeta\in C\), the value \(f(\zeta)\) is called the radial limit of \(f\) at \(\zeta\) if \(f (r\zeta)\to f(\zeta)\) as \(r\to 1-\). Let \(E_f\) denote the set of points \(\zeta\in C\) at which \(f\) has a radial limit. It
Cantón, A. +2 more
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Borel sets and Ramsey's theorem
Journal of Symbolic Logic, 1973Definition 1. For a set S and a cardinal κ,In particular, 2ω denotes the power set of the natural numbers and not the cardinal 2ℵ0. We regard 2ω as a topological space with the usual product topology.Definition 2. A set S ⊆ 2ω is Ramsey if there is an M ∈ [ω]ω such that either [M]ω ⊆ S or else [M]ω ⊆ 2ω − S.Erdös and Rado [3, Example 1, p.
Fred Galvin, Karel Prikry
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An absoluteness principle for Borel sets
The Journal of Symbolic Logic, 1998The purpose of these notes is to describe an absoluteness principle due to Jacques Stern and discuss some applications to the general study of Borel sets. This paper will not be engaged in independence results, but in proving outright theorems about the Borel hierarchy.Roughly speaking, Stern's absoluteness principle states that if a certain set can ...
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Borel sets and circuit complexity
Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83, 1983It is shown that for every k, polynomial-size, depth-k Boolean circuits are more powerful than polynomial-size, depth-(k−1) Boolean circuits. Connections with a problem about Borel sets and other questions are discussed.
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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1965
Abstract The descriptive theory of Borel sets is developed for a fairly general class of spaces. For a satisfactory theory it seems to be necessary to work with a Hausdorff space subject to the condition that each open set can be expressed as a countable union of closed sets. Under this condition it is shown that the descriptive Borel
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Abstract The descriptive theory of Borel sets is developed for a fairly general class of spaces. For a satisfactory theory it seems to be necessary to work with a Hausdorff space subject to the condition that each open set can be expressed as a countable union of closed sets. Under this condition it is shown that the descriptive Borel
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Borel Sets, Random Variables, and Borel Functions
1990In Chapter 3, we note that the class of events is assumed to be a sigma algebra of subsets of the basic space Ω. In Appendix 2a, we characterize a sigma algebra of events as a class closed under complements and countable unions, and show that these conditions imply closure under countable intersections.
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