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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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How can the simply typed lambda calculus be Turing-incomplete, yet stronger than second-orde...
Simply typed lambda calculus and simple type theory are not equivalent. The former only has rules for alpha- and beta-reduction, the latter also has rules for Modus Ponens, extensionality and the Intr …