Separating bounded arithmetical theories by Herbrand consistency

The problem of Π1−separating the hierarchy of bounded arithmetic has been studied in the paper. It is shown that the notion of Herbrand Consistency, in its full generality, cannot Π1−separate the theory I∆0 + ∧ j Ωj from I∆0; though it can Π1−separate I∆0 + Exp from I∆0. This extends a result of L. A. Ko lodziejczyk (2006), by showing the unprovability of the Herbrand Consistency of I∆0 in the theory I∆0 + ∧ j Ωj. vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv 2010 Mathematics Subject Classification: Primary 03F30, 03F25; Secondary 03F05, 03F40.