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Large small sets. (English) Zbl 0687.03033

J. Mycielski has shown [Colloq. Math. 20, 71-76 (1969; Zbl 0203.057)] that there exists a measure zero and first category set containing a translated copy of every countable set of reals. We show that if \(MA_{\kappa}\) holds, a similar set exists for every set of reals of cardinality \(\kappa\).
Reviewer: P.Komjáth

MSC:

03E50 Continuum hypothesis and Martin’s axiom
03E05 Other combinatorial set theory
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets

Citations:

Zbl 0203.057
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