 Here, transitivity is the well-known property that for all worlds \(w_1\), \(w_2\), \(w_3\) in \(W\), if \(w_1 Rw_2\) and \(w_2 Rw_3\), then \(w_1 Rw_3\). A relation is conversely well-founded iff there are no infinite ascending sequences, that is sequences of the form \(w_1 Rw_2 Rw_3 R \ldots\). Note that conversely well-founded frames are also irreflexive, for if \(wRw\), this gives rise to an infinite ascending sequence \(wRwRwR\ldots\).