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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 a probability theory developed in intuitionistic logic?
There is a probability theory developed in Łukasiewicz logic.
If you understand the french (and if you are still interested):
http://www.brunodefinetti.it/Opere/logiquedelaProbabilite.pdf