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Mundici, Daniele

Duality between logics and equivalence relations. (English) Zbl 0497.03018

Trans. Am. Math. Soc. 270, 111-129 (1982).
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Cited in 1 Review
Cited in 4 Documents

MSC:

03C30 Other model constructions

Keywords:

Robinsons’s consistency theorem
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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] C. C. Chang and H. J. Keisler, Model theory, 2nd ed., North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Studies in Logic and the Foundations of Mathematics, 73. · Zbl 0276.02032
[3] S. Feferman, Two notes on abstract model theory. I, Fund. Math. 82 (1974), 153-165. · Zbl 0296.02026
[4] J. Flum, First-order logic and its extensions, \?ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974) Springer, Berlin, 1975, pp. 248 – 310. Lecture Notes in Math., Vol. 499.
[5] Harvey Friedman, One hundred and two problems in mathematical logic, J. Symbolic Logic 40 (1975), 113 – 129. · Zbl 0318.02002 · doi:10.2307/2271891
[6] Per Lindström, On extensions of elementary logic, Theoria 35 (1969), 1 – 11. · Zbl 0206.27202 · doi:10.1111/j.1755-2567.1969.tb00356.x
[7] J. Donald Monk, Mathematical logic, Springer-Verlag, New York-Heidelberg, 1976. Graduate Texts in Mathematics, No. 37. · Zbl 0354.02002
[8] J. A. Makowsky and S. Shelah, The theorems of Beth and Craig in abstract model theory. I. The abstract setting, Trans. Amer. Math. Soc. 256 (1979), 215 – 239. · Zbl 0428.03032
[9] -, Positive results in abstract model theory (preprint).
[10] J. A. Makowsky, Saharon Shelah, and Jonathan Stavi, \?-logics and generalized quantifiers, Ann. Math. Logic 10 (1976), no. 2, 155 – 192. · Zbl 0346.02007 · doi:10.1016/0003-4843(76)90021-8
[11] Daniele Mundici, An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman’s fourth problem, J. Symbolic Logic 46 (1981), no. 3, 523 – 530. · Zbl 0465.03020 · doi:10.2307/2273754
[12] Daniele Mundici, Robinson’s consistency theorem in soft model theory, Trans. Amer. Math. Soc. 263 (1981), no. 1, 231 – 241. · Zbl 0519.03031
[13] -, Compactness \( = JEP\) in any logic, Fund. Math. 116 (1982) (to appear).
[14] Daniele Mundici, Applications of many-sorted Robinson consistency theorem, Z. Math. Logik Grundlag. Math. 27 (1981), no. 2, 181 – 188. · Zbl 0463.03023 · doi:10.1002/malq.19810271103
[15] -, Compactness, interpolation and Friedman’s third problem (to appear). · Zbl 0495.03020
[16] -, Embeddings, amalgamation and elementary equivalence (to appear). · Zbl 0599.03038
[17] Mark E. Nadel, An arbitrary equivalence relation as elementary equivalence in an abstract logic, Z. Math. Logik Grundlag. Math. 26 (1980), no. 2, 103 – 109. · Zbl 0444.03016 · doi:10.1002/malq.19800260703
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