**
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