  Imposing the requirement of a compactly generated future Cauchy  horizon has not only the negative virtue of excluding some unsuited  candidate time machine spacetimes but a positive virtue as well. It  is easily proved that if \(H^+ (\Sigma_0)\)  is compactly generated then the condition of strong  causality is violated on  \(H^+ (\Sigma_0)\), which means,  intuitively, there are almost closed causal curves near   \(H^+ (\Sigma_0)\).[17]  This violation can be taken as an indication that the seeds of CTCs  have been planted on \(\Sigma_0\) and that by the time  \(H^+ (\Sigma_0)\) is reached they are ready to bloom.