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Making doughnuts of Cohen reals

✍ Scribed by Lorenz Halbeisen

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
153 KB
Volume
49
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

For a βŠ† b βŠ† Ο‰ with b\ a infinite, the set D = {x ∈ [Ο‰]^Ο‰^ : a βŠ† x βŠ† b} is called a doughnut. A set S βŠ† [Ο‰]^Ο‰^ has the doughnut property π’Ÿ if it contains or is disjoint from a doughnut. It is known that not every set S βŠ† [Ο‰]^Ο‰^ has the doughnut property, but S has the doughnut property if it has the Baire property ℬ︁ or the Ramsey property β„›. In this paper it is shown that a finite support iteration of length Ο‰~1~ of Cohen forcing, starting from L, yields a model for CH + $ \sum ^1 _2 $(π’Ÿ) + $ \neg \sum ^1 _2 $(ℬ︁) + $ \neg \sum ^1 _2 $(β„›).

πŸ“œ SIMILAR VOLUMES

What is left of CH after you add Cohen r
What is left of CH after you add Cohen reals?
✍ I. JuhΓ‘sz; L. Soukup; Z. SzentmiklΓ³ssy πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 710 KB

The principle CH\* concerning elementary submodels is formulated and is shown to be valid in any generic extension obtained by adding any number of Cohen reals to a ground model satisfying CH. CH\* has interesting topological consequences, e.g.: (i) Every initially wl-compact, countably tight 7'3 s