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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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From elementary equivalence to isomorphism
A few years ago, when I took the basic course in Logic, I was very surprised to discover that given a signature $\sigma$ and two structures $M$ and $N$ of $\sigma$ which are elementarily equivalent (t …