The Geometry of L^k-Canonization I: Rosiness from Efficient Constructibility
| Autor: | Hill, Cameron Donnay |
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| Rok vydání: | 2012 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages |
| Databáze: | arXiv |
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