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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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Natural statements independent from true $\Pi^0_2$ sentences
If computability counts, Turing famously showed that if M is a Turing machine equipped with an oracle for the regular halting problem, then M's own halting problem is undecidable by M. And if M2 is a …