# Some additive properties of sets of real numbers

```@article{Erds1981SomeAP,
title={Some additive properties of sets of real numbers},
author={Paul Erd{\"o}s and Kenneth Kunen and R. Daniel Mauldin},
journal={Fundamenta Mathematicae},
year={1981},
volume={113},
pages={187-199}
}```
• Published 1981
• Mathematics
• Fundamenta Mathematicae
Some problems concerning the additive properties of subsets of R are investigated. From a result of G. G . Lorentz in additive number theory, we show that if P is a nonempty perfect subset of R, then there is a perfect set M with Lebesgue measure zero so that P+M = R. In contrast to this, it is shown that (1) if S is a subset of R is concentrated about a countable set C, then A(S+R) = 0, for every closed set P with A(P) = 0 ; (2) there are subsets G, and G s of R both of which are subspaces of…
Some properties of Borel subgroups of real numbers
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• Mathematics
• 2007
D. H. Fremlin and J. Jasiński [4] have proved a relative consistency of the existence of a very thin set of reals. In this context they have asked (private communication) the following question:
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• Mathematics
J. Symb. Log.
• 1998
These results extend: Fremlin and Miller's theorem that strong measure zero sets having Hurewicz's property have Rothberger's property, Galvin and Miller’s theorem that the algebraic sum of a set with the γ-property and of a first category set is aFirst category set, and Bartoszyfnski and Judah's characterization of -sets.
COMPLEXITY OF INDEX SETS OF DESCRIPTIVE SET-THEORETIC NOTIONS
• Mathematics, Computer Science
• 2018
A generalization of computability theory, admissible recursion theory, is applied to consider the relative complexity of notions that are of interest in descriptive set theory, and it is demonstrated that there is a separation of descriptive complexity between the perfect set property and determinacy for analytic sets of reals.

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