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.
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