A dichotomy in classifying quantifiers for finite models

Saharon Shelah; Mor Doron

doi:10.2178/jsl/1129642126

Published online by Cambridge University Press: 12 March 2014

Saharon Shelah and

Mor Doron

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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:

Corresponding

E-mail address:

shelah@math.huji.ac.il ;

mord@math.huji.ac.il

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.

References

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A dichotomy in classifying quantifiers for finite models

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