随机图的所有约简都是模型完全的
All reducts of the random graph are model-complete
摘要：
研究了随机图的自同构群所包含的局部闭变换幺半群。我们证明了这样的变换幺半群是由幺半群中的置换局部生成的，或者包含常数运算，或者包含将随机图内射映射到诱导子图的运算，该子图是团或独立集。作为一个推论，我们的技术产生了一个新的证明西蒙托马斯的分类的五个封闭的超群的自同构群的随机图;我们的证明使用不同的拉姆齐理论工具比一个由托马斯，也许是更简单。由于所考虑的幺半群是随机图中可定义的关系结构的自同态幺半群，我们能够得出几个模型理论的推论：我们的结果的一个后果是，随机图中具有一阶定义的所有结构都是模型完备的。此外，我们得到了这些结构的分类存在的互定义性。
英文摘要：
We study locally closed transformation monoids which contain the automorphism group of the random graph. We show that such a transformation monoid is locally generated by the permutations in the monoid, or contains a constant operation, or contains an operation that maps the random graph injectively to an induced subgraph which is a clique or an independent set. As a corollary, our techniques yield a new proof of Simon Thomas' classification of the five closed supergroups of the automorphism group of the random graph; our proof uses different Ramsey-theoretic tools than the one given by Thomas, and is perhaps more straightforward. Since the monoids under consideration are endomorphism monoids of relational structures definable in the random graph, we are able to draw several model-theoretic corollaries: One consequence of our result is that all structures with a first-order definition in the random graph are model-complete. Moreover, we obtain a classification of these structures up to existential interdefinability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
