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The equivalence of the disjunction and existence properties for modal arithmetic
Published online by Cambridge University Press: 12 March 2014
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.
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- Research Article
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- Copyright © Association for Symbolic Logic 1989