Topological representation for monadic implication algebras

• Autorzy: Abad Manuel , Cimadamore Cecilia , Díaz Varela José
• Języki publikacji: EN

Abstrakty

EN

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.

Słowa kluczowe

EN

Implication algebra; Monadic Boolean algebra; Implication spaces; Dual categorical equivalence

Kategorie tematyczne

• 06E15: Stone spaces (Boolean spaces) and related structures
• 06F99: None of the above, but in this section
• 03G25: Other algebras related to logic

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 299-309

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

Abad Manuel

• Departamento de Matemática, Universidad Nacional del Sur and Universidad Nacional del Comahue, Neuquen, Argentina

autor

Cimadamore Cecilia

• Departamento de Matemática, Universidad Nacional del Sur and Universidad Nacional del Comahue, Neuquen, Argentina

autor

Díaz Varela José

• Departamento de Matemática, Universidad Nacional del Sur and Universidad Nacional del Comahue, Neuquen, Argentina

Bibliografia

• [1] Abad M., Díaz Varela J.P., Zander M., Varieties and quasivarieties of monadic Tarski algebras, Sci. Math. Jpn., 2002, 56(3), 599–612
• [2] Abad M., Díaz Varela J.P., Torrens A., Topological representation for implication algebras, Algebra Universalis, 2004, 52, 39–48 http://dx.doi.org/10.1007/s00012-004-1872-2[Crossref]
• [3] Abad M., Monteiro L., Savini S., Seewald J., Free monadic Tarski algebras, Algebra Universalis, 1997, 37, 106–118 http://dx.doi.org/10.1007/s000120050006[Crossref]
• [4] Abbott J.C., Implicational algebras, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 1967, 11(59), 3–23
• [5] Burris S., Sankappanavar H.P., A course in universal algebra, Graduate Texts in Mathematics 78, Springer-Verlag, New York-Berlin, 1981
• [6] Cignoli R., Quantifiers on distributive lattices, Discrete Mathematics, 1991, 96, 183–197 http://dx.doi.org/10.1016/0012-365X(91)90312-P[Crossref]
• [7] Halmos P.R., Algebraic logic I, Monadic Boolean algebras, Compositio Math., 1956, 12, 217–249
• [8] Halmos P.R., Free monadic algebras, Proc. Amer. Math. Soc., 1959, 10, 219–227 http://dx.doi.org/10.2307/2033581[Crossref]
• [9] Halmos P.R., Algebraic logic, Chelsea Publishing Co., New York, 1962
• [10] Iturrioz L., Monteiro A., Représentation des algèbres de Tarski monadiques, preprint
• [11] Koppelberg S., Handbook of Boolean algebras, North-Holland Publishing Co., Amsterdam, 1989

Identyfikatory

DOI

10.2478/s11533-009-0002-y