Weakly Borel-complete topological spaces
Michael Rice, George Reynolds (1980)
Fundamenta Mathematicae
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Michael Rice, George Reynolds (1980)
Fundamenta Mathematicae
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Vassilios Gregoriades (2012)
Fundamenta Mathematicae
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We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show that under some conditions the emerging parameters can be chosen in a hyperarithmetical way and using this we obtain some uniformity results.
H. Sarbadhikari (1977)
Fundamenta Mathematicae
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Miloslav Duchoň (1974)
Matematický časopis
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Dana Scott (1964)
Fundamenta Mathematicae
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R. Purves (1966)
Fundamenta Mathematicae
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J. Büchi (1955)
Fundamenta Mathematicae
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Alessandro Andretta, Donald A. Martin (2003)
Fundamenta Mathematicae
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Two sets of reals are Borel equivalent if one is the Borel pre-image of the other, and a Borel-Wadge degree is a collection of pairwise Borel equivalent subsets of ℝ. In this note we investigate the structure of Borel-Wadge degrees under the assumption of the Axiom of Determinacy.
Alexey Ostrovsky (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Alexey Ostrovsky (2011)
Fundamenta Mathematicae
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Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.