## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, January 23, 2019 — 3:30 PM EST

**Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo**

"The Isomorphism Problem for Pregeometries"

We will talk about the isomorphism problem for classes of r.i.c.e. pregeometries. By a r.i.c.e. pregeometry we mean a computable structure $\mathcal{M}$ equipped with a r.i.c.e. operator $cl^{\mathcal{M}}$ such that $(\mathcal{M},cl^{\mathcal{M}})$ is a pregeometry. The operator $cl^{\mathcal{M}}$ is called r.i.c.e. (relatively intrinsically computably enumerable) if for every computable copy $(\mathcal{N},cl^{\mathcal{N}})$ of $(\mathcal{M},cl^{\mathcal{M}})$, $cl^{\mathcal{N}}$ is c.e. in $\mathcal{N}$. We will show that if $K$ is a class of r.i.c.e. pregeometries in which dependent elements are dense, then the isomorphism problem for the class $K$ is $\Pi^0_3$-hard.

MC 5413

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.