Title: Priority arguments in descriptive set theory
by Andrew Marks (UCLA) as part of Computability theory and applications

Abstract
We give a new characterization of when a Borel set is
Sigma^0_n complete for n at at least 3. This characterization is
proved using Antonio Montalb’an’s true stages machinery for
conducting priority arguments.

As an application, we prove the decomposability conjecture in
descriptive set theory assuming projective determinacy. This
conjecture characterizes precisely which Borel functions are
decomposable into a countable union of continuous functions with
$Pi^0_n$ domains. Our proof also uses a theorem of Leo Harrington
that assuming the axiom of determinacy there is no $omega_1$ length
sequence of distinct Borel sets of bounded rank. This is joint work
with Adam Day.