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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.
8
votes
Complete mathematics
Presberger arithmetic is used in practice for software verification, e.g. to prove that a program fragment is free of array subscript overflows. Basically the program has expressions like a[3*i+k] an …