Submission date: 30 October 2012.

Abstract:

We demonstrate that for the k-variable theory T of a finite structure (satisfying certain amalgamation conditions), if finite models of T can be recovered from diagrams of finite {\em subsets} of model of T in a certain “efficient” way, then T is rosy -- in fact, a certain natural \aleph_0-categorical completion T^{lim} of T is super-rosy of finite U^\thorn-rank. In an appendix, we also show that any k-variable theory T of a finite structure for which the Strong L^k-Canonization Problem is efficient soluble has the necessary amalgamation properties up to taking an appropriate reduct.

Mathematics Subject Classification:

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Full text arXiv 1210.7882: pdf, ps.