Friday, April 8, 201612:30 pmModel theory seminarGC 6417

# The Lattice of Definable Equivalence Relations in Homogeneous n-Dimensional Permutation Structures

## Samuel Braunfeld

### Rutgers University

In 2002, Cameron classified the homogeneous permutations (structures in a language of 2 linear orders). In working toward the classification the homogeneous n-dimensional permutation structures (structures in a language of n linear orders), consideration of the lattice of definable equivalence relations leads to a generalization of Cameron’s structures, giving a large class of new homogeneous examples, and places some constraints on lattices that can appear.