Heyting Algebras

<p>This book presents an English translation of a classic Russian text on duality theory</p><p>for Heyting algebras. Written by Georgian mathematician Leo Esakia the text proved</p><p>popular among Russian-speaking logicians. This translation helps make the ideas</p><p>accessible to a wider audience and pays tribute to an influential mind in mathematical</p><p>logic. </p><p><br></p><p>The book discusses the theory of Heyting algebras and closure algebras as</p><p>well as the corresponding intuitionistic and modal logics. The author introduces the</p><p>key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke</p><p>frames) resulting in the structures now known as Esakia spaces. The main theorems</p><p>include a duality between the categories of closure algebras and of hybrids and a duality</p><p>between the categories of Heyting algebras and of so-called strict hybrids.</p><p><br></p><p>Esakia’s book was originally published in 1985. It was the firstof a planned two-volume monograph</p><p>on Heyting algebras. But after the collapse of the Soviet Union the publishing house</p><p>closed and the project died with it. Fortunately this important work now lives on in</p><p>this accessible translation. The Appendix of the book discusses the planned contents</p><p>of the lost second volume.</p><div><br></div><p></p>