This is a continuation of my Math Colloquium talk from Sep 12, 2001. The questions I will discuss are about first order effectiveness in arithmetic and algebraic geometry. For instance, can one express by a first order sentence the fact that tr.deg.Q(t,u)=2, or detect the isomorphy type of Q(t,u) among all the fuction fields of varieties over Q? The prerequisites for this talk are just honors algebra level (but the proofs -which I will go into- invove very deep mathematics).