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The classical theorem of Chevalley states that projections of Zariski closed sets are Zariski constructible (finite union of locally closed sets). This result follows from simple model theoretic arguments; it is so called ''quantifier elimination''. Number of quantifiers in a defining formula measures how complicated a set is. Quantifier elimination (for algebraically closed fields) can be interpreted to state that ''anything algebraic is as simple as it gets''. In many model theoretic settings, there is an interplay between quantifier elimination and existence of a ''tame'' topology. In this talk, we describe a Noetherian topology extending the Zariski topology which sheds some new light on the study of pairs of algebraically closed fields. Basic model theoretic requirements and the meaning of ''pairs of algebraically closed fields'' will be explained in the first half of the talk.