منابع مشابه
Small Forcings and Cohen Reals
We show that all posets of size א1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of results.
متن کاملInfinite Powers and Cohen Reals
We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Zω acts like a permutation of the coordinates almost everywhere. Furthermore, this permutation varies continuously. This shows that a result of Dow and Pearl is sharp, and gives some insight into an open problem of Terada. Our example Z is simply the set of ω1 Cohen reals, viewed as ...
متن کاملMaharam Algebras and Cohen Reals
We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah [14] we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real.
متن کاملMaking doughnuts of Cohen reals
For a ⊆ b ⊆ ω with b \ a infinite, the set D = {x ∈ [ω] : a ⊆ x ⊆ b} is called a doughnut. A set S ⊆ [ω] has the doughnut property D , if it contains or is disjoint from a doughnut. It is known that not every set S ⊆ [ω] has the doughnut property, but S has the doughnut property if it has the Baire property B or the Ramsey property R . In this paper it is shown that a finite support iteration o...
متن کاملStrong Measure Zero Sets Without Cohen Reals
If ZFC is consistent, then each of the following are consistent with ZFC + 20 = א2: 1. X ⊆ IR is of strong measure zero iff |X| ≤ א1 + there is a generalized Sierpinski set. 2. The union of א1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size א2. 1 The authors thank the Israel Foundation for Basic Research, Israel Academy of Science. 2 Publi...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 1997
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2275741