@article {IOPORT.04095444,
    author       = {Friedman, Harvey and Sheard, Michael},
    title        = {The disjunction and existence properties for axiomatic systems of truth.},
    year         = {1988},
    journal      = {Annals of Pure and Applied Logic},
    volume       = {40},
    number       = {1},
    issn         = {0168-0072},
    pages        = {1-10},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/0168-0072(88)90038-3},
    abstract     = {This is a sequel to the authors' earlier paper [ibid. 33, 1-21 (1987; Zbl 0634.03058)]. There they considered various extensions of Peano arithmetic enriched by the truth predicate T( ), and accompanying axioms and rules. Here they address themselves to the problem: in which of these extensions do the truth disjunction property and the truth existence property [if $\vdash \exists x T\#A(x)$ then $\vdash T\#A(n)$ for some numeral n] hold? Very roughly, their results are as follows. On the negative side, if the system satisfies U-inf[$\forall x T(A(x))\to T(\forall x A(x))]$ or T-comp[TA$\vee T(\neg A)]$, then it lacks both properties or T(A) is provable for all A. The positive side: For a system R, let ${\frak M}(R)=<\underset \tilde{}\to N,\{\#A/R\vdash T(\#A)\}>$. If $R\subseteq S$ and ${\frak M}(R)\vDash S$, then S has both properties. And so, the authors work with rather simple systems R's (e.g. ``primitive recursive arithmetic'') and complicated S's. In the last section, they comment on the conjecture that the disjunction property implies the existence property. ``This conjecture is far more reasonable than it might at first appear'', they state. Indeed, they proved the corresponding facts for the intuitionistic and modal systems.},
    reviewer     = {M.Yasuhara},
    identifier   = {04095444},
}