A Modeltheoretic Solution to a Problem of Tarski

Let 1 n. We show that the class NrnCAβ of n-dimensional neat reducts of β-dimensional cylindric algebras is not closed under forming elementary subalgebras. This solves a long-standing open problem of Tarski and his co-authors Andreka, Henkin, Monk and Nemeti. The proof uses genuine model-theoretic arguments.

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