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Mathematics > Logic

arXiv:math/0405091 (math)
[Submitted on 6 May 2004]

Title:A dichotomy in classifying quantifiers for finite models

Authors:Mor Doron, Saharon Shelah
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Abstract: We consider a family U of finite universes. The second order quantifier Q_R, means for each u in 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 Q_R, ever Q_R is interpretable by quantifying over subsets of u and one to one functions on u both of bounded order, or the logic L(Q_R) (first order logic plus the quantifier Q_R) is undecidable.
Subjects: Logic (math.LO)
Report number: Shelah [DoSh:801]
Cite as: arXiv:math/0405091 [math.LO]
  (or arXiv:math/0405091v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.math/0405091

Submission history

From: Saharon Shelah's Office [view email] [via SHLHETAL proxy]
[v1] Thu, 6 May 2004 03:03:56 UTC (32 KB)
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