论文标题
非标准有限组的完整类型合并
Complete type amalgamation for non-standard finite groups
论文作者
论文摘要
我们扩展了先前在Hrushovski的稳定器定理上的工作，并证明了Pillay-Scanlon-Wagner在三种类型的产品上的众所周知的衡量理论版本。这概括了Gowers对三组产品的结果，并产生了Quasirandom组现有渐近结果的模型理论证明。我们还获得了Roth定理的模型理论证明，内容涉及在适当可定义的可融合基团中的正密度子集的长度$ 3 $的存在，例如无参与的可数符合的Abelian群体和有限的Abelian Abelian obelian obs Odd Order的无互动和超级企业。
We extend previous work on Hrushovski's stabilizer's theorem and prove a measure-theoretic version of a well-known result of Pillay-Scanlon-Wagner on products of three types. This generalizes results of Gowers on products of three sets and yields model-theoretic proofs of existing asymptotic results for quasirandom groups. We also obtain a model-theoretic proof of Roth's theorem on the existence of arithmetic progressions of length $3$ for subsets of positive density in suitable definably amenable groups, such as countable amenable abelian groups without involutions and ultraproducts of finite abelian groups of odd order.
