TY - JOUR
T1 - A dichotomy in classifying quantifiers for finite models
AU - Shelah, Saharon
AU - Doron, Mor
PY - 2005/12
Y1 - 2005/12
N2 - We consider a family U of finite universes. The second order existential quantifier Qℜ, means for each U ∈ U 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.
AB - We consider a family U of finite universes. The second order existential quantifier Qℜ, means for each U ∈ U 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.
UR - http://www.scopus.com/inward/record.url?scp=32244444050&partnerID=8YFLogxK
U2 - 10.2178/jsl/1129642126
DO - 10.2178/jsl/1129642126
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AN - SCOPUS:32244444050
SN - 0022-4812
VL - 70
SP - 1297
EP - 1324
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 4
ER -