Marczewski–Burstin Representations of Boolean Algebras Isomorphic to a Power Set

Volume 53 / 2005

Artur Bartoszewicz Bulletin Polish Acad. Sci. Math. 53 (2005), 239-250 MSC: 28A05, 06E25, 03E20. DOI: 10.4064/ba53-3-1


The paper contains some sufficient conditions for Marczewski–Burstin representability of an algebra $\cal A$ of sets which is isomorphic to $\mathcal P(X)$ for some $X$. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to $\mathcal P (X)$ and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.


  • Artur BartoszewiczInstitute of Mathematics
    Łódź Technical University
    Wólczańska 215, I-2
    93-005 Łódź, Poland

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