## 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

### Keywords:

Martin’s axiom; measure zero and first category set

Zbl 0203.057
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