Ultrafilters and combinatorial number theory
Ultrafilters and combinatorial number theory
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超滤器和组合数论
DOI：
10.1007/bfb0062706
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
N. Hindman
中科院分区：
文献类型：
--
作者：
N. Hindman
我们关注的是数学的两个领域，以及它们之间可能令人惊讶的密切联系。一个是组合数论的分支，它研究在给定ℕ的有限划分的情况下，在该划分的一个单元中找到某些描述的和或乘积的能力。另一个是集合论拓扑学的分支，研究ℕ上具有特定性质的超滤子的存在性。我们将提出并在可行的情况下证明我们熟悉的前一个领域的那些主要结果和后一个领域的许多相关结果。
Our concern is with two areas of mathematics and a, possibly surprising, intimate connection between them. One is the branch of combinatorial number theory which deals with the ability, given a finite partition of ℕ, to find sums or products of certain descriptions lying in one cell of that partition. The other is the branch of set theoretic topology dealing with the existence of ultrafilters on ℕ which have specified properties. We shall present and, to the extent feasible, prove those major results in the former area with which we are familiar and many of the related results in the latter area.