Open Access
2000/2001 On Marczewski-Burstin Representations of Certain Algebras of Sets
Marek Balcerzak, Artur Bartoszewicz, Krzysztof Ciesielski
Real Anal. Exchange 26(2): 581-592 (2000/2001).


We show that the Generalized Continuum Hypothesis GCH (its appropriate part) implies that many natural algebras on $\mathbb{R}$, including the algebra $\mathcal{B}$ of Borel sets and the interval algebra $\Sigma$, 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 $\mathbb{R}$ which are not MB-representable. We prove that some algebras (including $\mathcal{B}$ and $\Sigma$) 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.


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Marek Balcerzak. Artur Bartoszewicz. Krzysztof Ciesielski. "On Marczewski-Burstin Representations of Certain Algebras of Sets." Real Anal. Exchange 26 (2) 581 - 592, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1012.28002
MathSciNet: MR1844137

Primary: 03E35
Secondary: 28A05

Keywords: Borel sets , Continuum hypothesis , MB-representation , ultrafilters

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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