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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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Borel / Wadge hierarchies on subsets closed under prepending a finite prefix
I'm interested in subsets $X$ of the Cantor space ($2^\omega$) or the Baire space ($\omega^\omega$) that are closed under prepending an arbitrary finite prefix:
$$
(x_1, x_2, \dots) \in X \implies (s_ …