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Abstract: We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier Q in FO(Q_k), the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two FO(Q_1)-equivalent models with certain additional structure, yields a pair of FO(Q_k)-equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity and... (Update)
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.... a class C and its complement are closed under stretching, and there are A 2 C and B 62 C as above, then C is not definable in L1 (Q u ) [26]. This argument shows that graph properties such as planarity and 3 colorability are not definable in L1 (Q u ) Hanf s technique...
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BibTeX entry: (Update)
L. Hella and J. Nurmonen. Vectorization hierarchies of some graph quantifiers. Archive for Mathematical Logic, to appear. http://citeseer.ist.psu.edu/325350.html More
@misc{ hella-vectorization,
author = "L. Hella and J. Nurmonen",
title = "Vectorization hierarchies of some graph quantifiers",
note = "Archive for Mathematical Logic, to appear.",
url = "citeseer.ist.psu.edu/325350.html" }
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