Andrew Marks

The decomposability conjecture

We characterize which Borel functions are decomposable into
a countable union of functions which are piecewise continuous on
\Pi^0_n domains, assuming projective determinacy. One ingredient of
our proof is a new characterization of what Borel sets are \Sigma^0_n
complete. Another important ingredient is a theorem of Harrington that
there is no projective sequence of length \omega_1 of distinct Borel
sets of bounded rank, assuming projective determinacy. This is joint
work with Adam Day.