A Note on Gödel-Dummet Logic LC

Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow A_{n})\vee (A_{n}\rightarrow A_{0})\) is equivalent to Gödel-Dummett logic LC. However, if \(n\) is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.