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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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Propositional logic and first order logic textbook
Not quite a textbook, but a collection of historical projects about elementary logic and
related issues in discrete mathematics and computer science can be found at
www.cs.nmsu.edu/historical-projects …