Calculus on strong partition cardinals

The assumption of [HM] and our assumption here, the existence of a strong partition cardinal, is moderately special. On the one hand, it violates the Axiom of Choice and is not relatively consistent with ZF (unlike AC and its negation). On the other hand, under the Axiom of Determinacy (AD), such cardinals are abundant and consistent with countable choice and DC, the principle of Dependent Choices. א1, for example, is a strong partition cardinal and there are strong partition cardinals that are the limits of strong partition cardinals. AD itself, while once considered unimaginably powerful, seems fairly tame now by the yardstick of the large cardinal axiom hierarchy (well below supercompact cardinals in consistency strength). See [Ka] for details.