## 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

Thursday, June 20, 2019 10:00 AM EDT

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

"The Isomorphism Problem of the Class of Computable Trees of Finite Rank"

We discussed before the isomorphism problem of the class $K_n$ of computable trees of rank $n$ for every natural number $n$, which we showed to be $\Pi_{2n}-$complete. Now we are looking at the class $K_{<\omega}$ of all computable trees of finite rank. We could show that the isomorphism problem of that class is complete with respect to the class of sets of the form $\bigcup_{n\in\omega}A_n$ where $A_i\subseteq A_{i+1}$, $A_i$ is $\Sigma^0_i$, and there exists a sequence of co-c.e.\ sets $\{C_m\}_{m\in\omega}$ such that $C_i\subseteq C_{i+1}$ and $C_i\cap A_m=A_i$ for all $i\leq m$.

MC 5479

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 co-ordinated within our Office of Indigenous Relations.