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Et W 1> W2, W 3, . . qui l et aux axiomes correspondent respectivement aux axiomes d'extensionaite multiplicatifs (ou axiomes du choix) pour les types 1, 2, 3, . on a egale­ ment wo(V1 ) = wo(V2 ) = wo(V3 ) = . . = wo ( Wl ) = wo(W2) = = w0(W8) = . . = u. (iv) D'autre part, pour les expressions X1, X2, X8, .. correspondant aux axiomes de description ou de pseudo-definition ( et qui representent, en quelque sorte, l'axiome de reductibilite S)), on trouve wo(Xd = wo (X2) = = wo(Xs) = . . = v.

V O N WRIGHT A NEW SYSTEM OF MODAL LOGIC The system outlined in the present paper differs from the "classical" systems of modal logic in that it employs the notion of relative modality. We introduce the symbol M(p/q). It can be read: p is possible, given q. Accordingly, ""M(p/q) can be read : p is impossible, given q; and -M(-"'p/q) can be read : p is necessary, given q. The letters p and q stand for arbitrary propositions. The letter t will be used to represent an arbitrary tautology of propositional logic (PL).

Mostowski 5) avait introduit a '1) L. Henkin, Completeness in the theory of types. JSL 15 (1950), pp. 81-91. '2) A. Tarski, Some notions and methods on the borderline of algebr� _and metamathematics. Proceedings of the International Congress of Mathemat1c1ans, vol. I (1950) pp. 705-720. 'ensemble des modl:les, qui est a Ia base de notre pnnctpe (i). Cf. 5). B) K. Godel, The consistency of the continuwn hypothesis. Princeton 1940 (second printing, 1951). 4) E. W. Beth, Existence of complete models for extensions of the first-order predicate calculus.

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A Handbook for Designing Mathematics Laboratory in Schools by Hukum Singh


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