Abstract
Following the strategy in [15] to develop inconsistent models for relevant arithmetics, we formulate a connexive variant of arithmetic by replacing the conditional of RM3 with the Belikov–Loginov conditional. We obtain thus the connexive logic cRM3 which serves as a base logic for arithmetics cRM3ⁱ, cRM3ⁱ♯, cRM♯, cRMnⁱ ,and cRMω. We compare these with their counterparts RM3ⁱ♯, RM♯ and RMω that extend relevant arithmetic R♯.