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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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Compactness of existential second order logic and definability of certain quantifiers
A stronger logic than ESO, namely FO(H) - first order logic with all Henkin quantifiers, does not define countability. This is so because in empty vocabulary it has Skolem-Loewenheim property. Leszek …