Consistency of max{e, b} < e*

Establish whether it is consistent with ZFC that max{e, b} < e*, where e is the evasion number for ordinary prediction, b is the bounding number, and e* is the evasion number for bounding-prediction.

Background

The paper introduces variants of the evasion/prediction numbers, including the bounding-prediction versions e* and pr*. The main results separate many such characteristics, but the status of stricter separations involving e* remains unresolved.

The author explicitly points out that, even though models with e < b and b < e are known, the stronger separation max{e, b} < e* is still unknown.