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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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Essential reads in the philosophy of mathematics and set theory
The Foundations of Mathematics (FOM) mailing list has fair amount of interesting discussion with references worth following, plus a lot of lameness like anything else on the internet. Browsing its ar …