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Maximal logics. (English) Zbl 0415.03025


MSC:

03C95 Abstract model theory
18B99 Special categories
03C20 Ultraproducts and related constructions
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References:

[1] K. Jon Barwise, Axioms for abstract model theory, Ann. Math. Logic 7 (1974), 221 – 265. · Zbl 0324.02034 · doi:10.1016/0003-4843(74)90016-3
[2] Jon Barwise, Back and forth through infinitary logic, Studies in model theory, Math. Assoc. Amer., Buffalo, N.Y., 1973, pp. 5 – 34. MAA Studies in Math., Vol. 8.
[3] Miroslav Benda, On reduced products and filters, Ann. Math. Logic 4 (1972), 1 – 29. · Zbl 0235.02049 · doi:10.1016/0003-4843(72)90010-1
[4] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973. · Zbl 0276.02032
[5] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 211. · Zbl 0298.02004
[6] S. Garavaglia, Completeness for topological languages, Notices Amer. Math. Soc. 22 (1975), A-473. Abstract #75T-E36.
[7] -, Model theory of topological structures, Doctoral Dissertation, Yale Univ., New Haven, Ct., 1976.
[8] H. J. Keisler, Formulas with linearly ordered quantifiers. The syntax and semantics of infinitary languages, Springer-Verlag, Berlin and New York, 1969.
[9] Finn V. Jensen, Interpolation and definability in abstract logics, Synthese 27 (1974), 251 – 257. On the foundations of mathematics (Colloq., Second Finnish Summer School in Math. Logic, Helsinki, 1973). · Zbl 0311.02024 · doi:10.1007/BF00660898
[10] Per Lindström, On extensions of elementary logic, Theoria 35 (1969), 1 – 11. · Zbl 0206.27202 · doi:10.1111/j.1755-2567.1969.tb00356.x
[11] T. A. McKee, Infinitary logic and topological homeomorphisms, Z. Math. Logik Grundlagen Math. 21 (1975), no. 5, 405 – 408. · Zbl 0341.02013
[12] Joseph Sgro, Completeness theorems for topological models, Ann. Math. Logic 11 (1977), no. 2, 173 – 193. · Zbl 0387.03010 · doi:10.1016/0003-4843(77)90016-X
[13] Joseph Sgro, Completeness theorems for continuous functions and product topologies, Israel J. Math. 25 (1976), no. 3-4, 249 – 272. · Zbl 0344.54006 · doi:10.1007/BF02757004
[14] -, The decision problem for \( L(I)\), the interior operator logic (in preparation).
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