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Stone duality between boolean algebras and inverse limits of ÿnite sets is extended to a duality between locally ÿnite MV-algebras and a category of multisets naturally arising as inverse limits of ÿnite multisets.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The Johns Hopkins University Press is collaborating with JSTOR to digitize, preserve and extend access to American Journal of Mathematics.We are concerned here with the development of techniques, like those of algebraic geometry, but directly applicable to the study of differential geometry. A. Grothendieck in 1957 [3] introduced Affine Schemes, which are a concrete specification of the dual of the category of commutative rings. In this way he was able to glue them together to construct geometric objects. This came after the realization that the most general object of study in algebraic geometry was something locally identifiable with an object equal to the formal categorical dual of a commutative ring. Schemes made possible to apply in algebraic geometry the concepts of differential geometry connected with infinitely small changes of points on an algebraic variety. For example, the Spec of the ring of dual numbers is an infinitesimal subscheme D of the algebraic line L, and the tangent space at a point x of an algebraic variety X is the set of maps t from D to X such that (0) = x. In particular, LD = L X L. F. W. Lawvere proposed in 1967 [11] an axiomatic approach to the category of schemes, abstracted from these developments, but intended to be applicable to differential geometry. He also set basic guidelines on how to construct models of his axioms. In the mid 70's, A. Kock, G. Reyes and G. Wraith [4-10] [13] started the development of this theory, to be called Synthetic Differential Geometry. E. Dubuc in 1978 [1] explicitly demonstrated its applicability to the study of ordinary smooth manifolds by introducing the notion of (fully) well adapted model, and constructing one. The purpose of this note is twofold: First, to incorporate differential geometry into the field of applicability of the techniques and tools of algebraic geometry; second, to construct a model of Synthetic Differential AMS (MOS) subject classification (1970). Primary 58A05; Secondary 14A15, 14AO5, 14A99.'This research supported in part by Matematisk Institut, Aarhus Universitet.