Consistency property and model existence theorem for second order negative languages with conjunctions and quantifications over sets of cardinality smaller than a strong limit cardinal of denumerable cofinality

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1. [1] J.L. Bell - A. B. SLOMSON, Models and ultraproducts: An introduction, North Holland, Amsterdam, 1969. Zbl0179.31402MR269486
2. [2] C.C. Chang, Two interpolation theorems, Proceedings of the Rome conference on model theory, Symposia Mathematica, vol. V, Academic Press, New York, 1970, pp. 5-19. Zbl0222.02008MR282819
3. [3] C.C. Chang - H.J. Kiesler, Model theory, North Holland, Amsterdam, 1973. 
4. [4] J. Green, Consistency property for uncountable finite-quantifier languages, Doctoral Dissertation, University of Maryland, 1972. 
5. [5] C.R. Karp, Languages with formulas of infinite length, Doctoral Dissertation, University of Southern California, 1959. 
6. [6] C.R. Karp, Languages with expressions of infinite length, North Holland, Amsterdam, 1964. Zbl0127.00901MR176910
7. [7] C.R. Karp, Infinite quantifier languages and ω-chain of models, to appear in the forthcoming Proceedings of the Tarski Symposium. Zbl0308.02016
8. [8] H.J. Keisler, Model theory for infinitary languages, North Holland, Amsterdam, 1971. Zbl0222.02064MR344115
9. [9] S. Maehara - G. Takeuti, Two interpolation theorems for a positive second order predicate calculus, Journal of Symbolic Logic, 36 (1971), pp. 262-270. Zbl0278.02013MR307876
10. [10] M. Makkai, On the model theory of denumerably long formulas with finite strings of quantifiers, Journal of Symbolic Logic, 34 (1969), pp. 437-459. Zbl0235.02050MR255383
11. [11] J.I. Malitz, Problems in the model theory of infinitary languages, Doctoral Dissertation, University of California, Berkeley, 1966. 
12. [12] E. Mendelson, Introduction to mathematical logic, VanNostrand, Princeton, 1964. Zbl0192.01901MR164867
13. [13] R.M. Smullyan, First order logic, Springer-Verlag, Berlin, 1968. Zbl0172.28901MR243994

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