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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
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Partition relation, almost a Ramsey cardinal?
This is not a complete answer, but clears up some of the confusion.
After a bit more research, the definition of $\kappa \rightarrow [\kappa]^{<\omega}_{\alpha,\beta}$ is not the one I stated. This i …