Editing Heyting algebra (section)

===Comparison to Lindenbaum algebras===
The constructions we have just given play an entirely analogous role with respect to Heyting algebras to that of [[Lindenbaum algebra]]s with respect to [[Boolean algebra (structure)|Boolean algebras]]. In fact, The Lindenbaum algebra ''B''<sub>''T''</sub> in the variables {''A''<sub>''i''</sub>} with respect to the axioms ''T'' is just our ''H''<sub>''T''∪''T''<sub>1</sub></sub>, where ''T''<sub>1</sub> is the set of all formulas of the form ¬¬''F''→''F'', since the additional axioms of ''T''<sub>1</sub> are the only ones that need to be added in order to make all classical tautologies provable.