### The decomposability conjecture

Logic and Set Theory Seminar

24th February 2021, 4:00 pm – 5:30 pm

Online via Zoom,

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.

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