Tony Martin proved in [Mar98] that the Axiom of Determinacy AD implies the Axiom of Blackwell Determinacy Bl-AD, and conjectured that the converse holds as well: Conjecture 1 The Axiom of Blackwell Determinacy Bl-AD implies the Axiom of Determinacy AD. Although Martin, Neeman and Vervoort in their [MarNeeVer03] have made considerable progress on Martin’s Conjecture 1, the full conjecture remain...

Abstract One prominent criticism of the abstractionist program is so-called Bad Company objection. The complaint that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some them are inconsistent. most notorious example, course, Frege’s Basic Law V. A common response objection suggests an principle can used legitimately theory precisely when i...