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 Andr\'eka, 
Henkin, Monk, and N\'emeti. The construction we use when  alpha  is infinite 
also settles a conjecture of Tarski in the affirmative.