Homogeneous perfect binary trees
Perfect binary trees typically have highly inhomogeneous branches; for example, if a perfect tree
is computable, then for any set A there is a branch of higher degree than A. I will examine
properties such that it is possible to construct perfect binary trees every branch of which have
the property. Furthermore, I will show conditions on the frequency of branching that permit or
preclude the construction of such a tree. I will also survey other recent research in computability
theory and its applications.