IP set (source code)
= IP set
{c}
{title2=$\operatorname{FS}(x_1,x_2,\ldots)\subseteq A$}
A subset $A$ of the <positive integers> is an IP set if it contains a <finite-sums set> generated by an infinite sequence of positive integers. Sums use distinct indices, although the generators themselves need not be distinct. An IP set is necessarily infinite, because its successive partial sums are unbounded. The <partition regularity of IP sets> is the relative form of the <Hindman theorem> needed when applying that theorem inside an already specified IP set.
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