## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, January 11, 2019 — 10:00 AM EST

**Ruizhang Jin, Pure Mathematics, University of Waterloo**

"Model-theoretic Analysability in Differentially Closed Fields"

We are interested in types that are internal to or analysable in the constants in the theory of $DCF_0$. Using as a building block the well-known fact that the equation $\delta(\mathrm {log}\delta x)=0$ is analyzable in but not internal to the constants, we are able to construct analysable types with a unique canonical analysis such that each step of the analysis is of given $U$-rank. In addition, we look for criteria for when a 2-step analysable type is indeed internal. We develop a partial result when the binding group for the second step of the analysis is $\mathbb G_m(\mathcal C)$, the constant points of the multiplicative group: the type is internal if and only if the 2-step analysable type is (almost) the direct product of two types that are internal to the constants. However, the case is more complicated when the binding group for the second step is additive, as the previously mentioned criterion no longer holds.

Location

MC 5403

Canada

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University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1