 A third and fundamental step in the algebraic study of logics is to turn the set of formulas of a language \(L\) into an algebra, the algebra of formulas of \(L\), denoted by \(\bFm_L\). This algebra has the set of \(L\)-formulas as carrier and the operations are defined as follows. For every \(n\)-ary connective \(*\) with \(n \gt 0\), the function \(* ^{\bFm_L}\) is the map that sends each tuple of formulas \((\phi_1 , \ldots ,\phi_n)\) (where \(n\) is the arity of \(*\)) to the formula \(* \phi_1 \ldots \phi_n\), and for every 0-ary connective \(\dagger , \dagger^{\bFm_L}\) is \(\dagger\). If no confusion is likely we suppress the subindex in \(\bFm_L\) and write \(\bFm\) instead.