= IP-star filter
{c}
{title2=$\mathcal F_{\mathrm{IP}^{*}}$}
The <IP-star sets> form a proper <filter on a set> over the <positive integers>. Indeed, sets that are not <IP sets> are closed under taking subsets. They are also closed under finite unions, because the <partition regularity of IP sets> would otherwise put an IP set in one of the union's constituent sets. Taking complements gives upward closure and closure under finite intersections for the <IP-star sets>. The full set belongs to this filter and the empty set does not.
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