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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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How did the Baker-Gill-Solovay paper come to be?
Here is more about the result of M. Dekhtiar. There are several references to him proving the existence of an oracle $A$ with $P^{A} \ne NP^{A}$ (e.g. the Trakhtenbrot notes mentioned in another answe …