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Two notes on Ackermann's set theory

We give solutions to two problems which concern Ackermann's set theory, A.* This theory was introduced in [l] and it is now formulated in the first-order predicate calculus with identity, using e for membership and an individual constant, V, for the class of all sets. We use the letters φ, Φ, 0, and X to stand for formulae which do not contain V and capital Greek letters to stand for any formulae. Then the axioms of A are the universal closures of