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A Modeltheoretic Solution to a Problem of Tarski
Authors:Tarek Sayed Ahmed
Abstract:Let 1 < n < ω and β > 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.
Keywords:algebraic logic  cylindric algebras  neat reducts  elementary
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