A Modeltheoretic Solution to a Problem of Tarski

Mathematical Logic Quarterly 48 (3):343-355 (2002)
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Abstract

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 Andréka, Henkin, Monk and Németi. The proof uses genuine model-theoretic arguments

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