October 16
Su Gao,
Nankai University
The isomorphism relation for omnigenous locally finite groups
In 1959, P. Hall discovered a remarkable countable locally finite group $\mathbb{H}$ which is universal for all finite groups and has the ultrahomogeneity property. He showed that $\mathbb{H}$ is the unique group with these properties. An omnigenous locally finite group is defined by a weaker form of the ultrahomogeneity property. Nevertheless, we show that the class of all countable omnigenous locally finite groups has the maximum Borel cardinality of isomorphism types among all countable structures. This is joint work with Feng Li.