On the Relative Consistency Strength of Determinacy Hypothesis
Alexander S. Kechris, Robert M Solovay · Transactions of the American Mathematical Society · 1985
For any collection of sets of reals C, let C-DET be the statement that all sets of reals in C are determined. In this paper we study questions of the form: For given C ⊆ C', when is C'-DET equivalent, equiconsistent or strictly stronger in consistency strength than C-DET (modulo ZFC)? We focus especially on classes C contained in the projective sets.