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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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Algebraization of second-order logic
Did programme of predicate calculus algebraization succeed? In his essay An autobiography of polyadic algebras Halmos outlined why he is not satisfied with his baby. I suggest that Cylindric algebras …