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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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Finite versions of Godel' s incompleteness
It is important to include the axioms as well, since there is a theorem of logic that an axiom system can be changed equivalently so that any given proof can be made arbitrarily sorter, or on the cont …