Notation 5.30.
We denote by
\[\Sat(T), \qquad \SSat(T), \qquad \Acyc(T), \qquad \Mdl(T), \qquad\text{and}\qquad \Cong(T)\]
the partially ordered sets of saturated classes, strongly saturated classes, acyclic classes, modalities, and congruences in \(T\), with partial order given by inclusion. We regard a modality as its left class, giving inclusions \(\Mdl(T)\subseteq\Acyc(T)\subseteq\Sat(T)\), while \(\Cong(T)\subseteq\Acyc(T)\cap\SSat(T)\).