Regressive partition relations, \(n\)-subtle cardinals, and Borel diagonalization (Q1177036)

The author begins with a survey of regressive partition relations and their use in independence results, and states some related open questions. He studies further \(n\)-subtle cardinals and gives their characterization in terms of regressive partition relations requiring only a finite homogeneous set. Finally, he considers strengthenings of Friedman's Borel diagonalization propositions and characterizes their strengths in terms of \(n\)-subtle cardinals.