Weak forms of the Regularity Principle in the presence of IE_1

摘要

We study the strength of weak forms of the Regularity Principle in the presence of IE_1 (induction on bounded existential formulas) relative to other subsystems of PA. In particular, the Bounded Weak Regularity Principle is formulated, and it is shown that when applied to E_1 formulas, this principle is equivalent over IE_1 ~- to IΔ_0+exp.