Varieties of monadic heyting algebras. Part I

Studia Logica

Volumn 61, Issue 3, 1998, Pages 367-402

  Bezhanishvili, Guram ^a  

^a INSTITUTE OF PHYSICS   (Georgia)

Author keywords

Intuitionistic modal logic; Monadic filters; Monadic heyting algebras; Monadic ideals; Relatively complete subalgebras; Splittings

Indexed keywords

EID: 54649084820     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/A:1005073905902     Document Type: Article

References (47)

1. BEZHANISHVILI, G., 'Some results in monadic Heyting algebras', The Tbilisi Symposium on Logic, Language and Computation. Selected Papers. October 1995, Gudauri, Georgia, J. Ginzburg, Z. Khasidashvili, C. Vogel, J.-J. Levy and E. Valduvi (editors), 1997, CSLI, Stanford, p. 251-261.
2. BEZHANISHVILI, G., 'Varieties of monadic Heyting algebras. Part II: Duality theory' (to appear in Studia Logica).
3. BEZHANISHVILI, G., 'Varieties of monadic Heyting algebras. Part III.', 1997, Report fl IS-RR-97-0016F, JAIST.
4. BEZHANISHVILI, G., 'Splitting monadic Heyting algebras', 1997, Report jj IS-RR-970044F, JAIST.
5. BIRKHOFF, G., Lattice Theory, Providence, R. L, 1967.
6. BLOK, W. J., 'On the degree of incompleteness in modal logic and the covering relation in the lattice of modal logics', Report 78-07, Dept. of Math., University of Amsterdam, 1978.
7. BLOK, W. J., 'The lattice of modal logics: an algebraic investigation', Journal of Symbolic Logic 45 (1980), p. 221-236.
8. BULL, R. A., 'MIPC as the formalization of an intuitionist concept of modality', Journal of Symbolic Logic 31 (1966), p. 609-616.
9. BURRIS, S., and H. SANKAPPANAVAR, A Course in Universal Algebra, Graduate Texts in Mathematics 78, Springer-Verlag, New York - Heidelberg - Berlin, 1981.
10. COHN, P., Universal Algebra, Harper &c Row Publishers, New York - Evanston and London, 1965.
11. ESAKIA, L., 'Modal and superintuitionistic systems' (in Russian), in Logical Inference, p. 147-172, Nauka Press, Moscow, 1979.
12. ESAKIA, L. Heyting Algebras I. Duality Theory (in Russian), Metsniereba Press, Tbilisi, 1985.
13. FISHER SERVI, G., 'On modal logics with an intuitionistic base", Studia Logica 36 (1977), 141-149.
14. FISHER SERVI, G., 'Semantics for a class of intuitionistic modal calculi', in M. L. Dalla Chiara (ed.), Italian Studies in the Philosophy of Science, Reidel, Dordrecht, 1980, p. 59-72.
15. FISHER SERVI, G., 'Axiomatizations for some intuitionistic modal logics', Rend. Sem. Math. Univers. Polit. 42, 1984, p. 179-194.
16. GOLDBLATT, R., Topoi. The Categorical Analysis of Logic, North-Holland Publishing Company, Amsterdam - New York - Oxford, 1979.
17. GRÄTZER, G., General Lattice Theory, Akademie-Verlag, Berlin, 1978.
18. HALMOS, P. R., Algebraic Logic, Chelsea Publishing Company, New York, 1962.
19. JANKOV, V., 'Relationship between deducibility in the intuitionistic prepositional calculus and finite implicational structures' (in Russian), Dokl. Akad. Nauk SSSR 151 (1963), p. 1293-1294.
20. JANKOV, V., 'Constructing a sequence of strongly independent superintuitionistic prepositional calculi' (in Russian), Dokl. Akad. Nauk SSSR 181 (1968), p. 33-34.
21. JANKOV, V., 'Conjuctively indecomposable formulas in propositional calculi' (in Russian), Izv. Akad. Nauk SSSR 33 (1969), p. 18-38.
22. KRACHT, M., 'An almost general splitting theorem for modal logic', Studio, Logica 49 (1990), p. 455-470.
23. KRACHT, M., 'Prefinitely axiomatizable modal and intermediate logics', Mathematical Logic Quarterly 39 (1993), p. 301-322.
24. KRACHT, M., 'Splittings and the finite model property', Journal of Symbolic Logic 58 (1993), p. 139-157.
25. KUZNETSOV, A., and V. GERCIU, 'Superintuitionistic logics and finite approximability' (in Russian), Dokl. Akad. Nauk SSSR 195 (1970), p. 1029-1032.
26. MAC LANE, S., 'Categories for the Working Mathematician', Springer-Verlag, New York - Heidelberg Berlin, 1971.
27. MAKSIMOVA, L., 'On maximal intermediate logics with the disjunction property', Studio Logica 45 (1986), p. 69-75.
28. MALTSEV, A., Algebraic Systems (in Russian), Nauka Press, Moscow, 1970.
29. McKENZiE, R., 'Equational bases and nonmodular lattice varieties', Transactions of the, American Mathematical Society 174 (1972), p. 1-43.
30. MONTEIRO, A., 'Normalidad de las algebras de Heyting monádicas', Actas de las X Jornadas de la Union Matemdtica Argentina, Bahia Bianca, 1957, p. 50-51.
31. MONTEIRO, A., and O. VARSAVSKY, 'Algebras de Heyting monádicas', Actas de las X Jornadas de la Union Matemâtica Argentina, Bahia Bianca, 1957, p. 52-62.
32. ONO, H., 'Some results on the intermediate logis', Publications of Research Institute for Mathematical Sciences, Kyoto University 8 (1972), p. 117-130.
33. ONO, H., 'On some intuitionistic modal logics', Publications of Research Institute for Mathematical Sciences, Kyoto University 13 (1977), p. 687-722.
34. ONO, H., 'Model extension theorem and Craig's interpolation theorem for intermediate predicate logics', Reports on Mathematical Logic 15 (1983), p. 41-58.
35. ONO, H., 'Some problems in intermediate predicate logics', Reports on Mathematical Logic 21 (1987), p. 55-67.
36. ONO, H., and N.-Y. SUZUKI, 'Relations between intuitionistic modal logics and intermediate predicate logics', Reports on Mathematical Logic 22 (1988), p. 65-87.
37. RASIOWA, H., and R. SIKORSKI, The Mathematics of Metamathematics, PWN, Warszawa, 1963.
38. RAUTENBERG, W., 'Splitting lattice of logics', Archiv of Math. Logic 1980, p. 155-159.
39. SUZUKI, N.-Y., 'An algebraic approach to intuitionistic modal logics in connection with intermediate predicate logics', Studio, Logica 48 (1989), p. 141-155.
40. TROELSTRA, A. S., 'Ou intermediate propositional logics', Indagationes Mathematicae 27 (1965), p. 141-152.
41. WOLTER, F., Lattices of Modal Logics, PhD thesis, FU Berlin, 1993.
42. WOLTER, F., 'Superintuitionistic companions of classical modal logics', Studia Logica 58 (1997), p. 229-259.
43. WOLTER, F., 'The structure of lattices of subframe logics', Annals of Pure and Applied Logic 86 (1997), p. 47-100.
44. WOLTER, F., and M. ZAKHARYASCHEV, 'Intuitionistic modal logics as fragments of classical bimodal logics', in E. Orlowska (ed.), Logic at Work, Kluwer Academic Publishers, 1997 (in print).
45. WOLTER, F., and M. ZAKHARYASCHEV, 'On the relation between intuitionistic and classical modal logics', Algebra and Logic, 1996, p. 73-92.
46. WOLTER, F., and M. ZAKHARYASCHEV, 'Intuitionistic modal logics' (manuscript).
47. WRONSKI, A., 'Intermediate logics and the disjunction property', Reports on Mathematical Logic 1 (1973), p. 39-51.