The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra 𝓐 of sets which is isomorphic to 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 𝓟 (X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-1,
author = {Artur Bartoszewicz},
title = {Marczewski-Burstin Representations of Boolean Algebras Isomorphic to a Power Set},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {239-250},
zbl = {1113.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-1}
}
Artur Bartoszewicz. Marczewski-Burstin Representations of Boolean Algebras Isomorphic to a Power Set. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 239-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-1/