We show that the Generalized Continuum Hypothesis GCH (its appropriate part) implies that many natural algebras on R, including the algebra B of Borel sets and the interval algebra S, are outer Marczewski-Burstin representable by families of non-Borel sets. Also we construct, assuming again an appropriate part of GCH, that there are algebras on R which are not MB-representable. We prove that some algebras (including B and S) are not inner MB-representable. We give examples of algebras which are inner and outer MB-representable, or are inner but not outer MB-representable.
Proof of Theorem 7 from the paper has an error! We do not know if the theorem is true or false.
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Last modified November 16, 2003.