Journal of Symbolic Logic 54 (4):1456-1459 (1989)

Abstract
In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent
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DOI 10.2307/2274825
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Provability in Principle and Controversial Constructivistic Principles.Leon Horsten - 1997 - Journal of Philosophical Logic 26 (6):635-660.

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