The intuitionistic counterpart of PA: same axioms, but built over intuitionistic predicate logic. HA ⊢ φ ⇒ PA ⊢ φ but the converse fails (e.g. for ∀∃-statements unprovable constructively).
The intuitionistic counterpart of PA: same axioms, but built over intuitionistic predicate logic. HA ⊢ φ ⇒ PA ⊢ φ but the converse fails (e.g. for ∀∃-statements unprovable constructively).