EQUIVALENCE OF THE INDUCTION SCHEMA AND THE LEAST NUMBER PRINCIPLE FOR OPEN FORMULAS
Kiwamu Aoyama, Kenji Fukuzaki · SUT Journal of Mathematics · 1997
Let ℒA be the usual language for arithmetic. Let φ(x) be an ℒA-formula. φ(x) may contain free variables distinct from x as parameters. We consider the following two schemata. (Iφ(x)) φ(0)∧∀x(φ(x)→φ(x+1))→∀xφ(x),(Lφ(x)) ∃xφ(x)→∃x(∀y