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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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Non standard Algebraic Topology
As mentioned in the comments, the actual topology on the non-standard extension can be quite nasty. This is illustrated for example in the first set of problems in these notes. A solution is to replac …