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