Model Theory Seminar

Ruizhang Jin, Department of Pure Mathematics, University of Waterloo

"Constructing Analyzable Types in Differentially Closed Fields with Logarithmic Derivatives"

We generalize the well-known fact that the equation $\delta(\mathrm {log}\delta x)=0$ is analyzable in but not internal to the constants. We use the logarithmic derivative as a building block to construct analyzable types with a unique analysis of minimal length (up to interalgebraicity). We also look for criteria for a given definable set such that its pre-image under the logarithmic derivative is analyzable in but not internal to the constants.

MC 5403