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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 there any formal foundation to ultrafinitism?
I've always thought that assuming a formalist position (i.e., mathematics is merely the manipulation of symbols) easily allows for an ultrafinitist position. The formalist may easily grant that $b=10 …