MV-Algebras: Convergence and Duality
by
Roman Frič
Košice

MV-algebras generalize boolean algebras and, beside mathematical logic (many-valued reasoning), MV-algebras have been studied as fields of events in generalized probability theory ([1], [4]). For semisimple MV-algebras (also called archimedean) we define an initial sequential convergence and prove a Stone-type duality in which sequentially continuous MV-algebra homomorphiams are dual to generalized measurable maps. The duality can be viewed as a fuzzyfication of the boolean case (cf. [2], [3]). We mention some applications to the generalized probability.

References

[1] CIGNOLI, R., D'OTTAVIANO, I. M. L. and D. MUNDICI: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publ., Dordrecht, 2000.

[2] FRIC, R.: Sequential structures and probability: categorical reflections. Mathematik-Arbeitspapiere (Editor: Hans-E, Porst), Universität Bremen, Bremen, 48(1997), 157-169.

[3] FRIC, R.: A Stone-type duality and its applications to probability. Topology Proceedings, Vol. 22, Summer 1997 (Proceedings of the 12th Summer Conference on General Topology and its Applications, North Bay, August 1997), 125-137.

[4] RIECAN, B. and T. NEUBRUNN: Integral, Measure, and Ordering. Kluwer Acad. Publ., Dordrecht - Boston - London, 1997.

Date received: May 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-10.