Computability, orders, and groups

Orderable groups are extensively studied by logicians and group theorists. In my talk I will address aspects of left- or bi-orderable groups that are connected with computability theory. In particular, I will talk about constructions of bi-orderable computable groups that cannot be embedded into groups with computable bi-order. I will also discuss our recent work in progress with M. Steenbock about simplicity and computably left-orderability.