1. The classical introduction to a systematic modal model theory remains Segerberg [1971]. Some first applications of more sophisticated tools from classical model theory may be found in Fine [1975]. The algebraic connection was developed beyond the elementary level by L. Esakia, S. K. Thomason, R. I. Goldblatt and W. J. Blok. Two good surveys are Blok [1976] and Goldblatt [1976]. The proper perspective upon modal logic as a fragment of second-order logic was given in Thomason [1975]. An early appearance of correspondence theory proper is made in Sahlqvist [1975], full surveys are found in Van Benthem [1982a] for the case of modal logic and Van Benthem [1982b] for the case of tense logic. The other case studies are still in a preliminary state, with the exception of the intuitionistic treatise Rodenburg [1982].
2. Ajtai, M.: 1979, Isomorphism and higher-order equivalence’, Ann. Math. Logic. 16, 181–233.
3. Blok, W. J.: 1976, ‘Varieties of interior algebras’, dissertation, Mathematical Institute, University of Amsterdam.
4. Boolos, G.: 1979, The Unprovability of Consistency, Cambridge University Press, Cambridge.
5. Burgess, J. P.: 1979, ‘Logic and time’, J. Symbolic Logic 44, 566–582.