Andrew Marks : The decomposability conjecture

Posted by Filippo Calderoni , part of the Logic Seminar.

At

April 13, 2021, 4 p.m.

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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.