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2003-2004 Algebras with inner MB-representation.
Marek Balcerzak, Artur Bartoszewicz, Krzysztof Ciesielski
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Real Anal. Exchange 29(1): 265-273 (2003-2004).


We investigate algebras of sets, and pairs $(\mathcal{A , I})$ consisting of an algebra $\mathcal{A}$ and an ideal $\mathcal{I} \subset \mathcal{A}$, that possess an inner MB-representation. We compare inner MB-representability of $(\mathcal{A , I})$ with several properties of $(\mathcal{A , I})$ considered by Baldwin. We show that $\mathcal{A}$ is inner MB-representable if and only if $\mathcal{A} =S(\mathcal{A} \setminus\mathcal{H}(\mathcal{A}))$, where $S(\cdot)$ is a Marczewski operation defined below and $\mathcal H$ consists of sets that are hereditarily in $\mathcal{A}$. We study the question of uniqueness of the ideal in that representation..


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Marek Balcerzak. Artur Bartoszewicz. Krzysztof Ciesielski. "Algebras with inner MB-representation.." Real Anal. Exchange 29 (1) 265 - 273, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 9 June 2006

zbMATH: 1065.03033
MathSciNet: MR2061310

Primary: 06E25
Secondary: 28A05 , 54E52

Keywords: Algebra of sets , ideal of sets , Marczewski-Burstin representation

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 1 • 2003-2004
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