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Marczewski–Burstin representations vs. Bernstein and Dense subsets

Nowik A.

Demonstratio Mathematica

2016

Vol. 49, nr 4

372--378

We find values of superposition of Marczewski–Burstin operation and operation of finding Bernstein sets. Several counterexamples of Marczewski–Burstin systems are given.

Marczewski-Burstin representations of Boolean algebras isomorphic to a power set

Bartoszewicz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 3

239-250

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.