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. |