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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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Definitions of definable compactness
Both definitions are equivalent in o-minimal structures for any definable topology $\tau$ as long as either $\tau$ is Hausdorff or the underlying o-minimal structure has definable choice.
In general w …