Logic Seminar

Please note that the time is PST

In his thesis, Arant introduced and studied the notion of Borel graphability: an analytic equivalence relation E on X is Borel graphable if there is a Borel graph on X whose connectivity relation is equal to E. We will discuss two instances of Borel graphability with surprising properties. First, we will consider an equivalence relation arising from computability theory which is Borel graphable if and only if there is a non-constructible real. Second, we will explore the question of which Polish group actions have Borel graphable orbit equivalence relations and we will show that this is the case whenever the group is connected. This is joint work with Tyler Arant and Alekos Kechris.