The equivalence of the disjunction and existence properties for modal arithmetic
Harvey M. Friedman, Michael Sheard · Journal of Symbolic Logic · 1989
Abstract In a modal system of arithmetic, a theory S has the modal disjunction property if whenever S ⊢ □φ ∨ □ψ, either S ⊢ □φ or S ⊢ □ψ. S has the modal numerical existence property if whenever S ⊢ ∃x □φ(x), there is some natural number n such that S ⊢ □φ(n). Under certain broadly applicable assumptions, these two properties are equivalent.