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Maximal Deductive Systems and Injective Objects in the Category of Hilbert Algebras

1988; Wiley; Volume: 34; Issue: 3 Linguagem: Inglês

10.1002/malq.19880340305

1521-3870

Daniel Gluschankof, Miguel Tilli,

Logic, Reasoning, and Knowledge

Mathematical Logic QuarterlyVolume 34, Issue 3 p. 213-220 Article Maximal Deductive Systems and Injective Objects in the Category of Hilbert Algebras Daniel Gluschankof, Daniel Gluschankof Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428-Buenos Aires, ArgentinaSearch for more papers by this authorMiguel Tilli, Miguel Tilli Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428-Buenos Aires, ArgentinaSearch for more papers by this author Daniel Gluschankof, Daniel Gluschankof Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428-Buenos Aires, ArgentinaSearch for more papers by this authorMiguel Tilli, Miguel Tilli Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428-Buenos Aires, ArgentinaSearch for more papers by this author First published: 1988 https://doi.org/10.1002/malq.19880340305Citations: 9AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 Balbes, R., and P. Dwinger, Distributive Lattices. University of Missouri Press, Columbia, Mo., 1974. 2 Balbes, R., and A. Horn, Injective and projective Heyting algebras. Trans. A. M. S. 148 (1970) 549–559. 3 Bell, J. L., On the strength of the Sikorski Extension Theorem for Boolean algebras. J. Symbolic Logic 48 (1983) 841–845. 4 Bell, J. L., and D. H. Fremlin, The maximal ideal theorem for lattices of sets. Bull. London Math. Soc. 4 (1972) 1–2. 5 Diego, A., Sobre álgebras de Hilbert (Thesis). Notas de Lógica Matemática 12 (1965). Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca. 6 Gluschankof, D., and M. Tilli, On some extension theorem in functional analysis and the theory of Boolean algebras. To appear in Revista de la Unión Matemática Argentina. 7 Halpern, J. D., and A. Levy, The Boolean Prime Ideal Theorem does not imply the Axiom of Choice. AMS Proc. In Axiomatic Set Theory (1971) 83–134. 8 Johnstone, P. T., Stone Spaces. Cambridge University Press, Cambridge, 1982. 9 Klimovsky, G., El teorema de Zorn y la existencia de filtros e ideales maximales en los reticulados distributivos. Revista de la Unión Matemática Argentina 18 (1958) 160–164. 10 Luxemburg, W. A. J., A remark on Sikorski's extension theorem for homomorphisms in the theory of Boolean algebras. Fund. Math. 55 (1964) 239–247. 11 Monteiro, A., Unpublished lectures given at the Universidad Nacional del Sur, Bahía Blanca, in 1960–1961. 12 Monteiro, A., Sur les algèbres de Heyting symétriques. Portugaliae Mathematica 39 (1980), fasc. 1–4. 13 Rasiowa, H., and R. Sikorski, The Mathematics of Metamathematics. Warsaw, 1963. 14 Sikorski, R., A theorem on extension of homomorphisms. Ann. Soc. Pol. Math. 21 (1948) 332–335. Citing Literature Volume34, Issue31988Pages 213-220 ReferencesRelatedInformation