Logic Seminar

We give a Baire category characterization of when a subset
of a Polish space is \Sigma^0_{n+2}-hard for n > 0. Our proof uses a
priority argument, and Antonio Montalban's true stages machinery. We
apply this characterization to the decomposability conjecture; the
problem of describing when a function is a union of countably many
continuous functions defined on \Pi^0_n sets.