Sets containing productsets in stable groups
Sets containing productsets in stable groups
复制标题
包含稳定组中的乘积集的集合
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Isaac Goldbring
中科院分区：
文献类型：
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作者：
U. Andrews;G. Conant;Isaac Goldbring
We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the "productset property"). We show that the productset property holds for any definable subset $A$ of an expansion of a discrete amenable group such that $A$ has positive Banach density and the formula $xcdot yin A$ is stable. For arbitrary first-order expansions of groups, we consider a "$1$-sided" version of the productset property, which is characterized in various ways using coheir independence. For stable groups, the productset property is equivalent to this $1$-sided version, and behaves as notion of largeness for definable sets, which can be characterized by a natural weakening of model-theoretic genericity.
