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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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What is the status of irrational numbers within finitism/ultrafinitism?
Even while considering the universe to be finite, one can do mathematics symbolically as a game with a system of rules. If the game doesn't have enough pieces
we just add new pieces, with new properti …