# 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 (1976)

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

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topFerro, 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

top- [1] J.L. Bell - A. B. SLOMSON, Models and ultraproducts: An introduction, North Holland, Amsterdam, 1969. Zbl0179.31402MR269486
- [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] C.C. Chang - H.J. Kiesler, Model theory, North Holland, Amsterdam, 1973.
- [4] J. Green, Consistency property for uncountable finite-quantifier languages, Doctoral Dissertation, University of Maryland, 1972.
- [5] C.R. Karp, Languages with formulas of infinite length, Doctoral Dissertation, University of Southern California, 1959.
- [6] C.R. Karp, Languages with expressions of infinite length, North Holland, Amsterdam, 1964. Zbl0127.00901MR176910
- [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] H.J. Keisler, Model theory for infinitary languages, North Holland, Amsterdam, 1971. Zbl0222.02064MR344115
- [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] 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] J.I. Malitz, Problems in the model theory of infinitary languages, Doctoral Dissertation, University of California, Berkeley, 1966.
- [12] E. Mendelson, Introduction to mathematical logic, VanNostrand, Princeton, 1964. Zbl0192.01901MR164867
- [13] R.M. Smullyan, First order logic, Springer-Verlag, Berlin, 1968. Zbl0172.28901MR243994

## Citations in EuDML Documents

top- Ruggero Ferro, An analysis of Karp’s interpolation theorem and the notion of $k$-consistency property
- Ruggero Ferro, $\omega $-satisfiability, $\omega $-consistency property, and the downward Lowenheim Skolem theorem for ${L}_{k,k}$
- Stefano Baratella, Karp's interpolation theorem for some classes of infinitary languages
- Ruggero Ferro, Strong Maehara and Takeuti type interpolation theorems for ${L}_{k,k}^{2+}$
- Ruggero Ferro, $\lambda $-satisfiability, $\lambda $-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 $\lambda $
- Ruggero Ferro, Strong Maehara and Takeuti type interpolation theorems for ${L}_{k,k}^{2+}$
- Ruggero Ferro, Seq-consistency property and interpolation theorems

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