Abstract
We try to make a distinction between the idea of representing and that of interpreting a mathematical structure. We present a slight generalization of Di Nola’s Representation Theorem as to incorporate this point of view. Furthermore, we examine some preservation and functorial aspects of the Boolean power construction.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Burris, S.: Boolean powers. Algebra Univ. 5, 341–360 (1975)
Cignoli, R.L.O., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht, Boston, London (2000)
Di Nola, A.: Representation and reticulation by quotients of MV-algebras. Ricerche di Matematica 40, 291–297 (1991)
Drossos, C.A., Karazeris, P.: Coupling an MV-algebra with a Boolean algebra. Internat. J. Approx. Reason. 18, 231–238 (1998)
Gispert, J., Mundici, D.: MV-algebras: a variety for magnitudes with archimedean units. Algebra Univ. 53, 7–43 (2005)
Gluschankof, D.: Prime deductive systems and injective objects in the algebras of Łukasiewicz infinite valued logic. Algebra Univ. 29, 354–377 (1992)
Henson, C.W., Iovino, J.: Ultraproducts in Analysis. In: Henson, C.W., Iovino, J., Kechris, A.S., Odell, E. (eds.) Analysis and Logic, pp. 1–114. Cambridge University Press, Cambridge (2003)
Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)
Kusraev, A.G., Kutateladze, S.S.: Boolean valued analysis. Kluwer Acad. Publ., Dordrecht, Boston, London (1999)
Lawvere, F.W.: Categories of Space and of Quantity. In: Echeveria, J., et al. (eds.) The Space of Mathematics: Philosophical, Epistemological and Historical Explorations (International Symposium on Structures in Mathematical Theories. San Sebastian, Spain 1990), de Gruyter, Berlin, pp. 14–30 (1992)
Mansfield, R.: The theory of Boolean ultrapowers. Ann. Math. Logic 2, 297–323 (1971)
Mundici, D.: Interpretation of AF C ∗ -algebras in Łukasiewicz sentential calculus. Journal of Functional Analysis 65, 15–63 (1986)
Ozawa, M.: Boolean valued interpretation of Hilbert space theory. J. Math. Soc. Japan 35, 609–627 (1983)
Ozawa, M.: Boolean valued analysis and type I AW*-algebras. Proc. Japan Acad. 59A, 368–371 (1983)
Ozawa, M.: Boolean valued interpretation of Banach space theory and module structures of von Neumann algebras. Nagoya Math. J. 117, 1–36 (1990)
Potthoff, K.: Boolean ultrapowers. Arch. math. Logik 16, 37–48 (1974)
Takeuti, G.: Two applications of logic to mathematics. Princeton University Press, Princeton, NJ (1978)
Takeuti, G.: C ∗ -algebras and Boolean valued analysis. Japan J. Math. 9, 207–245 (1983)
Thayer, F.J.: Quasidiagonal C ∗ -algebras and nonstandard analysis, Arxiv preprint math.OA/0209292 (2002)
Torrens, A.: W-algebras which are Boolean products of members of SR[1] and CW-algebras. Studia Logica 46, 265–274 (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Drossos, C.A., Karazeris, P. (2007). A Note on Representing and Interpreting MV-Algebras. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-75939-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75938-6
Online ISBN: 978-3-540-75939-3
eBook Packages: Computer ScienceComputer Science (R0)