Tarek Sayed Ahmed

The class of neat reducts is not elementary

We show that for any pair of ordinals 1 < alpha < beta, the class of alpha-dimensional neat reducts of beta-dimensional cylindric algebras is not elementary. This solves a problem of Tarski, and his co-authors Andréka, Henkin, Monk, and Németi. The construction we use when alpha is infinite also settles a conjecture of Tarski in the affirmative.

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