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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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The existence of proper classes
Andreas Blass states that proper classes do not exist and emphasizes that this is only his philosophical opinion, and not a mathematical fact.(link text).
Is it really not a mathematical fact? I thin …