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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 the union of two conservative extensions of a theory conservative?
Background/Motivation
A theory T over a signature(language) Σ is a set of formulae over Σ. These formulae are called the non-logical axioms of T.
To talk about what is provable in T we can agree on Hi …