Linked bibliography for the SEP article "Infinitary Logic" by John L. Bell

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Aczel, P., 1973, “Infinitary Logic and the Barwise Compactness Theorem”, Proceedings of the 1971 Bertrand Russell Memorial Logic Conference (Uldum, Denmark), J. Bell, J. Cole, G. Priest, and A. Slomson (eds.), Leeds: Bertrand Russell Memorial Logic Conference, 234–277. (Scholar)
Barwise, J., 1967, Infinitary Logic and Admissible Sets. Ph.D. Thesis, Stanford University. (Scholar)
–––, 1973, “Back and Forth through Infinitary Logic. Studies in Model Theory”, in Studies in Mathematics (Volume 8), Buffalo: Mathematical Association of American, pp. 5–34. (Scholar)
–––, 1975, Admissible Sets and Structures, Berlin: Springer-Verlag. (Scholar)
Barwise, J. and S. Feferman (eds.), 1985, Handbook of Model-Theoretic Logics, New York: Springer-Verlag. (Scholar)
Baumgartner, J., 1974, “The Hanf number for complete L_ω₁,ω sentences (without GCH)”, Journal of Symbolic Logic, 39: 575–578. (Scholar)
Bell, J. L., 1970, “Weak Compactness in Restricted Second-Order Languages”, Bulletin of the Polish Academy of Sciences, 18: 111–114. (Scholar)
–––, 1972, “On the Relationship between Weak Compactness in L_{ω₁, ω}, L_{ω₁, ω₁}, and Restricted Second-Order Languages”, Archive for Mathematical Logic, 15: 74–78. (Scholar)
–––, 1974, “On Compact Cardinals”, Zeitschrift für Mathematical Logik und Grundlagen der Mathematik, 20: 389–393. (Scholar)
–––, 1981, “Isomorphism of Structures in S-toposes”, Journal of Symbolic Logic, 43 (3): 449–459. (Scholar)
Chang, C.C., 1968, “Some Remarks on the Model Theory of Infinitary Languages”. in The Syntax and Semantics of Infinitary Languages (Lecture Notes in Mathematics: Volume 72), J. Barwise (ed.), Springer-Verlag, Berlin, 36-63. (Scholar)
Dickmann, M. A., 1975, Large Infinitary Languages, Amsterdam: North-Holland. (Scholar)
Drake, F.R., 1974, Set Theory: An Introduction to Large Cardinals, Amsterdam: North-Holland Publishing Company. (Scholar)
Ellentuck, E., 1976, “Categoricity Regained”, Journal of Symbolic Logic, 41 (3): 639–643. (Scholar)
Hanf, W. P., 1964, Incompactness in Languages with Infinitely Long Expressions, Amsterdam: North-Holland. (Scholar)
Karp, C., 1964, Languages with Expressions of Infinite Length, Amsterdam: North-Holland. (Scholar)
–––, 1965, “Finite-Quantifier Equivalence” in The Theory of Models, J. Addison, L. Henkin, and A. Tarski (eds.), Amsterdam: North-Holland, 407–412. (Scholar)
Keisler, H. J., 1974, Model Theory for Infinitary Logic, Amsterdam: North-Holland. (Scholar)
Keisler, H. J., and Julia F. Knight, 2004, “Barwise: Infinitary Logic And Admissible Sets”, Journal of Symbolic Logic, 10(1): 4–36 (Scholar)
Kolaitis, P. and M. Vardi, 1992, “Fixpoint Logic vs. Infinitary Logic in Finite-Model Theory,” Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science (LICS '92), IEEE, pp. 46-57; available online, doi:10.1109/lics.1992.185518 (Scholar)
Kreisel, G., 1965, “Model-Theoretic Invariants, Applications to Recursive and Hyperarithmetic Operations”, in The Theory of Models, J. Addison, L. Henkin, and A. Tarski (eds.), Amsterdam: North-Holland, 190-205. (Scholar)
Kueker, D., 1975, “Back-and-forth arguments in infinitary languages”, in Infinitary Logic: In Memoriam Carol Karp (Lecture Notes in Mathematics: Volume 492), D. Kueker (ed.), Berlin: Springer-Verlag. (Scholar)
Lopez-Escobar, E. G. K., 1965, “An Interpolation Theorem for Infinitely Long Sentences”, Fundamenta Mathematicae, 57: 253–272. (Scholar)
–––, 1966, “On Defining Well-Orderings”, Fundamenta Mathematicae, 59: 13–21. (Scholar)
Makkai, M., 1977, “Admissible Sets and Infinitary Logic”, Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland, 233-282. (Scholar)
Morley, M., 1965, “Omitting Classes of Elements”, The Theory of Models, J. Addison, L. Henkin, and A. Tarski (eds.), Amsterdam: North-Holland, 265-273. (Scholar)
Nadel, M. 1985, “L_ω₁,ω and Admissible Fragments”, in J. Barwise and S. Feferman (eds.) 1985, 271–287. (Scholar)
Platek, R., 1966, Foundations of Recursion Theory, Ph.D. Thesis, Stanford University. (Scholar)
Scott, D., 1961, “Measurable Cardinals and Constructible Sets”, Bulletin of the Academy of Polish Sciences, 9: 521–524. (Scholar)
–––, 1965, “Logic with Denumerably Long Formulas and Finite Strings of Quantifiers”, The Theory of Models, J. Addison, L. Henkin, and A. Tarski (eds.), Amsterdam: North-Holland, 329-341. (Scholar)
Scott, D., and A. Tarski, 1958, “The sentential calculus with infinitely long expressions”, Colloquium Mathematicum, 16: 166–170. (Scholar)
Shelah, Saharon, 2012, “Nice infinitary logics”, Journal of the American Mathematical Society, 25: 395-427, available online, doi:10.1090/s0894-0347-2011-00712-1 (Scholar)
Tarski, A., 1939, “Ideale in völlständingen Mengenkörpern I”, Fundamenta Mathematicae, 32: 140–150. (Scholar)
–––, 1958, “Remarks on predicate logic with infinitely long expressions”, Colloquium Mathematicum, 16: 171–176. (Scholar)
–––, 1962, “Some problems and results relevant to the foundations of set theory”, in E, Nagel, P. Suppes and A. Tarski (eds.), Logic, Methodology and Philosophy of Science, Stanford: Stanford University Press, 123-135. (Scholar)
Ulam, S., 1930, “Zur Masstheorie in der algemeinen Mengenlehre”, Fundamenta Mathematicae, 16: 140–150. (Scholar)

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