On the canonicity of Sahlqvist identities. (English) Zbl 0810.03050

Summary: We give a simple proof of the canonicity of Sahlqvist identities, using methods that were introduced in a paper by the author and A. Tarski [Am. J. Math. 73, 891-939 (1951; Zbl 0045.315)].


03G25 Other algebras related to logic
03B45 Modal logic (including the logic of norms)
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)


Zbl 0045.315
Full Text: DOI


[1] W. J. Blok,The lattice of modal logics: an algebraic investigation J. Symbolic Logic 45 (1980), pp. 221-236. · Zbl 0436.03010
[2] K. Fine,Some connections between modal and elementary logic, Proc. Third Scandinavian Logic Symposium, Studies in Logic 82 (Stig Kanger ed), North Holland, 1975, pp. 15 ? 31. · Zbl 0316.02021
[3] R. Goldblatt,Varieties of complex algebras Annals of Pure and Applied Logic 44 (1989), pp. 173-242. · Zbl 0722.08005
[4] R. Goldblatt,The McKinsey axiom is not canonical J. Symbolic Logic 56 (1991), pp. 554-562. · Zbl 0744.03019
[5] L. Henkin,Extending Boolean operations Fund. Math. 22 (1970), pp. 723-752. · Zbl 0218.06004
[6] B. J?nsson, [a]The preservation theorem for Boolean algebras with operators, Proc. of the International Conference Honoring Garrett Birkhoff (K. Baker, E. T. Schmidt, R. Wille, ed’s), Darmstadt, Germany, June 13 ? 17, 1991, Springer-Verlag, to appear.
[7] B. J?nsson andA. Tarski,Boolean algebras with operators I Amer. J. Math. 73 (1951), pp. 891-939. · Zbl 0045.31505
[8] E. J. Lemmon,An Introduction to Modal Logic Amer. Phil. Quarterly Monograph Ser. Basil, Blackwell 1977. · Zbl 0388.03006
[9] J. C. C. McKinsey andA. Tarski,Some theorems about the sentential calculi of Lewis and Heyting J. Symbolic Logic 13 (1948), pp. 1-15. · Zbl 0037.29409
[10] H. Ribeiro,A remark on Boolean algebras with operators Amer. J. Math. 74 (1952), pp. 162-167. · Zbl 0049.15802
[11] R. de Rijke andY. Venema, [a]Sahlqvist’s Theorem for Boolean Algebras with Operators, Manuscript.
[12] H. Sahlqvist,Completeness and correspondence in the first and second order semantics of modal logic, Proc. Third Scandinavian Logic Symposium, Studies in Logic 82 (Stig Kanger ed), North Holland, 1975, pp. 110 ? 143. · Zbl 0319.02018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.