References
H. Andréka, T. Gergely andI. Németi, On universal algebraic construction of logics,Studia Logica 36 (1977), 9–47.MR 58 # 21599
H. Andréka andI. Németi, Łoś lemma holds in every category,Studia Sci. Math. Hungar. 13 (1978), 361–376.MR 82i: 03049
H. Andréka andI. Németi, Formulas and ultraproducts in categories,Beiträge zur Algebra und Geometrie 8 (1979), 133–151.MR 81m: 18004
H. Andréka andI. Németi, Injectivity in categories to represent all first order formulas, I,Demonstratio Math. 12 (1979), 717–732.MR 81h: 03082
R. Guitart andC. Lair, Calcul syntaxique des modèles et calcul des formulas internes,Diagrammes, Vol. 4, 1980.
L. Henkin, J. D. Monk, A. Tarski, H. Andréka andI. Németi,Cylindric set algebras (Lecture Notes in Mathematics, 883), Springer, 1981.Zbl 497. 03025
H. Herrlich andG. E. Strecker,Category theory, Allyn and Bacon, Boston, 1973.MR 50 # 2284
Bui Huy Hien,A kategóriaelméleti ultraszorzat-fogalommal kapcsolatos problémák (Problems concerning the category theoretic notion of ultraproducts), Budapest, 1981. (Dissertation for the candidate degree) (In Hungarian)
A. I. Mal'cev,Algebraic systems, Springer, Berlin, 1973.MR 50 # 1878
I. Németi, Connections between cylindric algebras and initial algebra semantics of CF languages,Mathematical logic in computer science (Proc. Colloq. Salgótarján, 1978) (Colloquia Math. Soc. Bolyai, 26), North-Holland, Amsterdam, 1981; 561–606.
I. Németi andI. Sain, Cone-implicational subcategories and some Birkhoff-type theorems,Contributions to universal algebra (Proc. Colloq. Esztergom, 1977) (Colloquia Math. Soc. Bolyai, 29), North-Holland, Amsterdam, 1981; 535–578.
I. Sain, There are general rules for specifying semantics: observations on abstract model theory,CL&CL Comput. Linguist. Comput. Lang. 13 (1979), 195–250.MR 81d: 03040
I. Sain, Finitary logics of infinitary structures are compact,Abstracts Amer. Math. Soc., issue 17, vol. 3, no. 3, 1982; 252.
I. Sain,Category theoretic model theory via injective trees, 1982. (Manuscript)
I. Sain andBui Huy Hien, In which categories are first order axiomatizable hulls characterizable by ultraproducts?Cahiers Topologie Géom. Différentielle 24 (1983), 215–222.
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Hien, B.H. Elementary classes in the injective subcategories approach to abstract model theory. Period Math Hung 15, 87–99 (1984). https://doi.org/10.1007/BF02109374
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DOI: https://doi.org/10.1007/BF02109374