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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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Exact consistency-strength of "all projective sets are Ramsey"
I wonder if the exact consistency strength of
"All projective sets have the Ramsey property"
is still open.
In Solovay's model, all sets have the Ramsey property, so the consistency strength of this …