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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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Godel 's Ladder: Undecidable PI_N sentences for N =2, 3, ......
The halting set relative to an oracle deciding $\Pi_{n-1}$ sentences, provides such a sentence. This set is $m$-complete for $\Pi_n$.