Journal of Symbolic Logic

The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic

Harvey Friedman and Michael Sheard

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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.

Article information

Source
J. Symbolic Logic, Volume 54, Issue 4 (1989), 1456-1459.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743110

Mathematical Reviews number (MathSciNet)
MR1026609

Zentralblatt MATH identifier
0706.03018

JSTOR
links.jstor.org

Citation

Friedman, Harvey; Sheard, Michael. The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic. J. Symbolic Logic 54 (1989), no. 4, 1456--1459. https://projecteuclid.org/euclid.jsl/1183743110


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