Hierarchies of Subsystems of Weak Arithmetic

We completely characterize the logical hierarchy of various subsystems of weak arithmetic, namely: ZR, ZR + N, ZR + GCD, ZR + Bez, OI + N, OI + GCD, OI + Bez.Comment: To appear in Set theory, Arithmetic, Philosophy: Essays in Memory of Stanley Tennenbaum (edited by J. Kennedy and R. Kossak), Cambridge University Press