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Literature Cited
K. Härtig, “Über einem Quantifikator mit zwei Wirkungs bereichen,” Colloquium on the Found. Math., Math. Machines and Their Appl., Tihany, 1962, Akademidi Kiado, Budapest (1965), pp. 31–36.
W. Issel, “Semantische Untersuchungen über Quantoren. 1,” Zeitschr. Math. Logik Grundl. Math.,15, No. 2, 353–358 (1969).
G. A. Fuhrken, “A remark on the Härtig quantifier,” Zeitschr. Math. Logik Grundl. Math.,18, No. 2, 227–228 (1972).
W. Hanf, “Some fundamental problems concerning languages with infinitely long expressions,” Doctoral Dissertation, Univ. Calif. (1962).
P. J. Cohen, Theory of Sets and the Continuum Hypothesis [Russian translation], Mir, Moscow (1969).
G. A. Fuhrken, “Skolem-type normal forms for first-order languages with a generalized quantifier,” Fund. Math.,54, No. 2, 291–302 (1964).
A. G. Pinus, “An assertion of the type of the Levenheim-Skolem theorem for a calculus with the Härtig quantifier,” Repts. Abstrs. Fourth All-Union Conf. Math. Logic [in Russian], Shtiintsa, Kishinev (1976), p. 114.
J. H. Schmerl, “An elementary sentence which has ordered models,” J. Symbolic Logic,37, No. 3, 521–530 (1972).
C. C. Chang, “Some remarks on the model theory of infinitary languages,” in: The Syntax and Semantics of Infinitary Languages, Springer-Verlag, Berlin-Heidelberg-New York (1968), pp. 36–63.
R. B. Jensen and C. R. Karp, “Primitive recursive set functions,” in: Axiomatic Set Theory, Part 1, Am. Math. Soc., Providence, Rhode Island (1971), pp. 143–176.
J. Barwise, “Infinitary logic and admissible sets,” J. Symbolic Logic,34, No. 2, 226–253 (1969).
J. Barwise and K. Kunen, “Hanf numbers for fragments of L∞, ω,” Israel J. Math.,10, No. 2, 306–320 (1971).
J. Barwise, “Implicit definability and compactness in infinitary languages,” in: The Syntax and Semantics of Infinitary Languages, Springer-Verlag, Berlin-Heidelberg-New York (1968), pp. 36–67.
S. A. Kripke, “Transfinite recursions on ordinals. II,” J. Symbol. Logic,29, No. 1, 161–162 (1964).
S. J. Garland, “Second-order cardinal characterizability,” in: Axiomatic Set Theory, Part 2, Am. Math. Soc., Providence, Rhode Island (1974), pp. 127–146.
W. P. Hanf and D. S. Scott, “Classifying inaccessible cardinals,” Notices Am. Math. Soc.,8, No. 3, 445 (1961).
K. Kunen, “Indescribability and the continuum,” in: Axiomatic Set Theory, Part 1, Am. Math. Soc., Providence, Rhode Island (1971), pp. 199–204.
A. Lévy, “The sizes of indescribable cardinals,” in: Axiomatic Set Theory, Part 1, Am. Math. Soc., Providence, Rhode Island (1971), pp. 205–219.
A. A. Zykov, “The problem of spectrum in the extended predicate calculus,” Izv. Akad. Nauk SSSR,17, No. 1, 63–76 (1953).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 19, No. 6, pp. 1349–1356, November–December, 1978.
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Pinus, A.G. Cardinality of models for theories in a calculus with a Härtig quantifier. Sib Math J 19, 949–955 (1978). https://doi.org/10.1007/BF00972801
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DOI: https://doi.org/10.1007/BF00972801