Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 05 October 2016, 17:00 hrs
Room: S17#04-05, Department of Mathematics, NUS
Speaker: Reese Johnston
Title: Computability of isolated paths in uncountable binary trees.
Abstract: Alpha-recursion theory has been a target of study for some time;
a defining feature is the exotic behavior that can occur for general
ordinals alpha. In this talk, we consider the particular, and
better-behaved, case in which alpha is omega-1, and approach a class of
problems well-studied in the classical case: Pi-0-1-classes in Cantor space.
Of particular interest, for reasons that will become apparent, are the
degrees available as isolated paths through computable binary trees
that are restricted to countable width only. In this talk, I will show
that the degrees of these paths can – unlike the classical case – be
noncomputable and may in fact have very high Turing degree.