## Logic Seminar

Andrew Marks

UCLA

The decomposability conjecture

**Abstract:**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.

Tuesday April 13, 2021 at 4:00 PM in Zoom