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Mathematics Colloquium – Dr. Achilles Beros

Author: las-digital | Image: las-digital

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.