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

Ruggero Ferro

Rendiconti del Seminario Matematico della Università di Padova (1976)

  • Volume: 55, page 123-141
  • ISSN: 0041-8994

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Ferro, Ruggero. "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." Rendiconti del Seminario Matematico della Università di Padova 55 (1976): 123-141. <http://eudml.org/doc/107584>.

@article{Ferro1976,
author = {Ferro, Ruggero},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {123-141},
publisher = {Seminario Matematico of the University of Padua},
title = {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},
url = {http://eudml.org/doc/107584},
volume = {55},
year = {1976},
}

TY - JOUR
AU - Ferro, Ruggero
TI - 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
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1976
PB - Seminario Matematico of the University of Padua
VL - 55
SP - 123
EP - 141
LA - eng
UR - http://eudml.org/doc/107584
ER -

References

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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

Citations in EuDML Documents

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  1. Ruggero Ferro, An analysis of Karp’s interpolation theorem and the notion of k -consistency property
  2. Ruggero Ferro, ω -satisfiability, ω -consistency property, and the downward Lowenheim Skolem theorem for L k , k
  3. Stefano Baratella, Karp's interpolation theorem for some classes of infinitary languages
  4. Ruggero Ferro, Strong Maehara and Takeuti type interpolation theorems for L k , k 2 +
  5. Ruggero Ferro, λ -satisfiability, λ -consistency property, the downward Lowenheim Skolem theorem, and the failure of the interpolation theorem for L k , k with k a strong limit cardinal of cofinality λ
  6. Ruggero Ferro, Strong Maehara and Takeuti type interpolation theorems for L k , k 2 +
  7. Ruggero Ferro, Seq-consistency property and interpolation theorems

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