A dichotomy in classifying quantifiers for finite models
Mor Doron and Saharon Shelah
Source: J. Symbolic Logic
Volume 70, Issue 4
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1129642126
Digital Object Identifier: doi:10.2178/jsl/1129642126
Mathematical Reviews number (MathSciNet): MR2194248
Zentralblatt MATH identifier: 1108.03040
John T. Baldwin Definable second order quantifiers, Model theoretic logics (J. Barwise and S. Feferman, editors), Perspectives in Mathematical Logic, Springer-Verlag,1985, pp. 446--478.
Mathematical Reviews (MathSciNet): MR819543
Haim Gaifman On local and nonlocal properties, Logic Colloquium '81 (J. Stern, editor), North Holland,1982, pp. 105--135.
Mathematical Reviews (MathSciNet): MR757024
I. A. Lavrov 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).
Mathematical Reviews (MathSciNet): MR157904
Saharon Shelah There are just four second-order quantifiers, Israel Journal of Mathematics, vol. 15 (1973), pp. 282--300.
Mathematical Reviews (MathSciNet): MR335237