@misc {IOPORT.00016881,
    author       = {Miglioli, Pierangelo and Moscato, Ugo and Ornaghi, Mario},
    title        = {First-order theories from a constructive ("naive") point of view: Constructive compatibility of mathematical and philosophical principles in a "large" deductive system.},
    howpublished = {Mathematical foundations, Proc. Meet., Siena/Italy 1987, Atti Incontri Logica Mat. 4, 99-113 (1988).},
    year         = {1988},
    abstract     = {[For the entire collection see Zbl 0724.00008.] The authors study first-order theories with various logics intermediate between classical and intuitionistic logic, hoping for applications of their work in computer science. A theory is called constructive if it enjoys the disjunction property and the explicit definability property. As the authors do not want to depart too far from classical logic they only consider intermediate logics that contain Kuroda's schema $\forall x\neg\neg A(x)\to\neg\neg\forall x A(x)$. To any set $T$ of first-order axioms, they define, by classical set-theoretic means, a set $Constr(T)$ of formulas that follow "constructively" from $T$. They observe that $Constr(T)$ is not given in an effective way and they set themselves the task to find effective subtheories of $Constr(T)$, some of which turn out to be closed under applications of some more intuitionistically invalid principles. The paper contains many definitions and not so many complete proofs, as the authors refer frequently to other papers of their own.},
    reviewer     = {W.Veldman (Nijmegen)},
    identifier   = {00016881},
}