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References
Lee W. Badger [1975], The Malitz quantifier meets its Ehrenfeucht game, Ph.D. Thessis, University of Colerado.
Adreas Baudisch [1975], Elimination of the quantifier Qα in the theory of Abelian groups, typescript.
J. L.Bell and A. B. Slomson [1971], Models and Ultraproducts: an Introduction, North-Holland, Amsterdam, second revised printing.
W. Brown [1971], Infinitary languages, generalized quantifiers and generalized products, Ph.D. Thesis, Dartmouth.
C. C. Chang [1965], A note on the two cardinal problem, Proc. Amer. Math. Soc. 16, pp. 1148–1155.
C. C. Chang and H. J. Keisler [1973], Model Theory, North-Holland, Amsterdam.
A. Ehrenfeucht [1961], An application of games to the completeness problem for formalized theories, Fund. Math. 49, 129–141.
R. Fraïssé [1954], Sur le classification des systems de relations, Pub. Sci. de l’Université d’Alger I, no I.
G. Fuhrken [1964], Skolem-type normal forms for first order languages with a generalized quantifier, Fund. Math. 54, 291–302.
[1965], Languages with the added quantifier “there exist at least X α” in The Theory of Models, edited by J. Addision, L. Henkin and A. Tarski, North-Holland, Amsterdam, 121–131.
H. Herre [1975], Decidability of the theory of one unary function with the additional quantifier “there exist Xα many”, preprint.
H. Herre and H. Wolter. [1975], Entscheidbarkeit von Theorien in Logiken mit verallgemeinerten Quantoren, Z. Math. Logik, 21, 229–246.
H. J. Keisler. [1968], Models with orderings, in Logic, Methodology and Philosophy of Science III, edited by B. van Rotselaar and J. F. Staal, North-Holland, Amsterdam, 35–62.
[1970], Logic with the quantifier “there exist uncountably many”, Annals Math. Logic, 1, 1–94.
H. Läuchli and J. Leonard. [1966], On the elementary theory of linear order, Fund. Math., 49, 109–116.
L. D. Lipner [1970], Some aspects of generalized quantifiers, Ph. D. Thesis, Berkeley.
M. H. Löb [1967], Decidability of the monadic predicate calculus with unary function symbols, J. Symbolic Logic, 32, 563.
R. MacDowell and E. Specker [1961], Modelle der Arithmetik, in Infinitistic Methods, Pergamon Press, Oxford, 257–263.
M. Morley and R. L. Vaught, [1962], Homogeneous universal models, Math. Scand., 11, 37–57.
A. Mostowski. [1957], On a generalization of quantifiers, Fund. Math., 44, 12–36.
M. O. Rabin [1969], Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc., 141, 1–35.
A. B. Slomson [1968], The monadic fragment of predicate calculus with the Chang quantifier in Proceeding of the Summer School in Logic Leeds 1967, edited by M.H. Löb, Springer Lecture Notes, 70, 279–301.
[1972], Generalized quantifiers and well orderings, Archiv. Math. Łogik, 15, 57–73.
W. Szmielew [1955], Elementary properties of Abelian groups, Fund. Math., 41, 203–271.
R. L. Vaught [1964], The completeness of logic with the added quantifier “there are uncountably many”, Fund. Math., 54, 303–304.
S. Vinner [1972], A generalization of Ehrenfeucht’s game and some applications, Israel J. Math., 12, 279–298.
M. Weese [1975], Zur Entscheidbarkeit der Topologie der p-adischen Zähkorper in Sprach mit Machtigkeitsquantoren, Thesis, Berlin.
[1975i], The undecidability of the theory of well-ordering with the quantifier I, preprint.
H. Wolter [1975], Eine Erweiterung der elementaren Prädikatenlogik anwendungen in der Arithmetik und anderen mathematischen Theorien, Z. Math. Logik, 19, 181–190.
[1975], Entscheidbarkeit der Arithmetik mit Addition und Ordnung in Logiken mit verallgemeinerten Quantoren, Z. Math. Logik, 21, 321–330.
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Slomson, A. (1976). Decision problems for generalized quantifiers — A survey. In: Marek, W., Srebrny, M., Zarach, A. (eds) Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski. Lecture Notes in Mathematics, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096905
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DOI: https://doi.org/10.1007/BFb0096905
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