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Mapping a set of reals onto the reals
Journal of Symbolic Logic 48 (3):575-584 (1983)
Abstract
In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1DOI
10.2307/2273449
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Citations of this work
Partition Forcing and Independent Families.Jorge A. Cruz-Chapital, Vera Fischer, Osvaldo Guzmán & Jaroslav Šupina - forthcoming - Journal of Symbolic Logic:1-23.
On countably perfectly meager and countably perfectly null sets.Tomasz Weiss & Piotr Zakrzewski - 2024 - Annals of Pure and Applied Logic 175 (1):103357.
Forcing with copies of the Rado and Henson graphs.Osvaldo Guzmán & Stevo Todorcevic - 2023 - Annals of Pure and Applied Logic 174 (8):103286.
Applying generic coding with help to uniformizations.Dan Hathaway - 2023 - Annals of Pure and Applied Logic 174 (4):103244.
Sierpiński-Zygmund functions that are Darboux, almost continuous, or have a perfect road.Marek Balcerzak, Krzysztof Ciesielski & Tomasz Natkaniec - 1997 - Archive for Mathematical Logic 37 (1):29-35.
References found in this work
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
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