he empty (top) theory
at the top of the lattice. The top theory is the closure of the empty
theory &#8211; it contains only tautologies or logical truths; i.e.,
expressions that are true in all models (it is &#8220;true of everything&#8221;).
Multiple expansions would reduce a (closed) theory to the full
inconsistent theory at the bottom of the lattice. The full inconsistent
theory is the closed theory consisting of all expressions; i.e.,
expressions that are true in no models (it is &#8220;true of nothing&