The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic

Friedman, Harvey; Sheard, Michael

J. Symbolic Logic, Tome 54 (1989) no. 1, p. 1456-1459 / Harvested from Project Euclid

Résumé

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.

Publié le : 1989-12-14
Classification:

@article{1183743110,
     author = {Friedman, Harvey and Sheard, Michael},
     title = {The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic},
     journal = {J. Symbolic Logic},
     volume = {54},
     number = {1},
     year = {1989},
     pages = { 1456-1459},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743110}
}

Friedman, Harvey; Sheard, Michael. The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic. J. Symbolic Logic, Tome 54 (1989) no. 1, pp.  1456-1459. http://gdmltest.u-ga.fr/item/1183743110/