差集的可嵌入性
Embeddability Properties of Difference Sets
摘要：
利用非标准分析方法证明了整数集差集$A-B$的可嵌入性。（如果$A$的每个有限配置在$B$中具有移位副本，则集合$A$是“可嵌入”到$B$中的。）作为我们主要定理的推论，我们改进了I.Z. Ruzsa关于差集的交的定理，以及Jin定理（由V.Bergelson，H. Fürstenberg和B. Weiss），其中给出了覆盖任意大区间所需的$A-B$的移位数的精确界。
英文摘要：
By using nonstandard analysis, we prove embeddability properties of difference sets $A-B$ of sets of integers. (A set $A$ is "embeddable" into $B$ if every finite configuration of $A$ has shifted copies in $B$.) As corollaries of our main theorem, we obtain improvements of results by I.Z. Ruzsa about intersections of difference sets, and of Jin's theorem (as refined by V. Bergelson, H. Fürstenberg and B. Weiss), where a precise bound is given on the number of shifts of $A-B$ which are needed to cover arbitrarily large intervals.
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