Results 161 to 170 of about 6,838,637 (208)
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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.
F. Galvin, K. Prikry
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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 ...
Anna Maria Bigatti, L Robbiano
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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 ...
G. Hjorth
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Definable Elements of Definable Borel Sets
Mathematical Notes, 2019Vassily Lyubetsky, V G Kanovei
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Borel sets and functions in topological spaces
Acta Mathematica Hungarica, 2010Jiří Spurny
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On the Equivalence of Borel Sets
Mathematical Notes, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON BOREL SETS IN FUNCTION SPACES WITH THE WEAK TOPOLOGY
Journal of the London Mathematical Society, 2003Roman Pol
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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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