Algebras with inner MB-representation


Marek Balcerzak, Artur Bartoszewicz, and Krzysztof Ciesielski

Real Anal. Exchange 29(2) (2003-2004), 265-273.

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

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Last modified May 26, 2004.