Priority arguments in descriptive set theory

Abstract: We give a new characterization of when a Borel set is Sigma^0_n complete for n at at least 3. This characterization is proved using Antonio Montalb\'an's true stages machinery for conducting priority arguments.

As an application, we prove the decomposability conjecture in descriptive set theory assuming projective determinacy. This conjecture characterizes precisely which Borel functions are decomposable into a countable union of continuous functions with $\Pi^0_n$ domains. Our proof also uses a theorem of Leo Harrington that assuming the axiom of determinacy there is no $\omega_1$ length sequence of distinct Borel sets of bounded rank. This is joint work with Adam Day.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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