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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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Is there a syntactic proof that first-order positive inductive definitions are conservative?
Every first-order positive inductive definition has a fixed point. It follows that, if the biconditional is thought of as an axiom in the language obtained from the background language by adding a new …