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Tuesday, February 21, 2006

**Abstract:** Let *p* be the generic type of δ_{1}(y)=δ_{2}^{2}(y) in DCF_{02}. We will prove two things about *p*. First, *U(p)*=ω but its Δ-type is 1 and typical Δ-dimension is 2. This shows that the lower bound in McGrail's thesis is false. We will point out the mistake in her proof. Second, by the first part, *p* is a regular type. We will show that it is not locally modular and it does not come from a field. That is, if *q* is the generic type of a definable field in DCF_{02}, then *p* and *q* are orthogonal.