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A dichotomy in classifying quantifiers for finite models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah  and
Mor Doron
Saharon Shelah
Affiliation:
The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, Jerusalem 91904, Israel Department of Mathematics, Hill Center-Busch Campus Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA, E-mail: shelah@math.huji.ac.il
Mor Doron
Affiliation:
The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, Jerusalem 91904, Israel Department of Mathematics, Hill Center-Busch Campus Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA, E-mail: shelah@math.huji.ac.il
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Abstract

We consider a family of finite universes. The second order existential quantifier Qℜ means for each U Є quantifying over a set of n(ℜ)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called interpretability. We show that for every Qℜ, either Qℜ is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or the logic L(Qℜ) (first order logic plus the quantifier Qℜ) is undecidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1297 - 1324
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1]Baldwin, John T., Definable second order quantifiers, Model theoretic logics (Barwise, J. and Feferman, S., editors), Perspectives in Mathematical Logic, Springer-Verlag, 1985, pp. 446–478.Google Scholar
[2]Gaifman, Haim, On local and nonlocal properties, Logic Colloquium '81 (Stern, J., editor). North Holland, 1982, pp. 105–135.Google Scholar
[3]Lavrov, I. A., The effective non-separability of the set of identically true formulae and the set of finitly refutable formulae for certain elementary theories, Algebra i Logika, vol. 2 (1963). no. 1, pp. 5–18, (Russian).Google Scholar
[4]Shelah, Saharon, There are just four second-order quantifiers, Israel Journal of Mathematics, vol. 15 (1973), pp. 282–300.CrossRefGoogle Scholar
[5]Shelah, Saharon, Classifying of generalized quantifiers, Around classification theory of models, Lecture Notes in Mathematics, no. 1182, Springer-Verlag, 1986. pp. 1–46.CrossRefGoogle Scholar
[6]Shelah, Saharon, On quantification with a finite universe, this Journal, vol. 65 (2000), pp. 1055–1075.Google Scholar