منابع مشابه
Strong measure zero sets in Polish groups∗
In the context of arbitrary Polish groups, we investigate the Galvin– Mycielski–Solovay characterization of strong measure zero sets as those sets for which a meager collection of right translates cannot cover the
متن کاملFinite Powers of Strong Measure Zero Sets
In a previous paper – [17] – we characterized strong measure zero sets of reals in terms of a Ramseyan partition relation on certain subspaces of the Alexandroff duplicate of the unit interval. This framework gave only indirect access to the relevant sets of real numbers. We now work more directly with the sets in question, and since it costs little in additional technicalities, we consider the...
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...
متن کاملOn effectively closed sets of effective strong measure zero
The strong measure zero sets of reals have been widely studied in the context of set theory of the real line. The notion of strong measure zero is straightforwardly effectivized. A set of reals is said to be of effective strong measure zero if for any computable sequence {εn}n∈N of positive rationals, a sequence of intervals In of diameter εn covers the set. We observe that a set is of effectiv...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2016
ISSN: 0019-2082
DOI: 10.1215/ijm/1506067289