Sheaves, Games, and Model Completions

This text investigates propositional intuistionistic and modal logics from an alternative point of view. It mainly deals with the structure of the category of finitely presented Heyting and modal algebras, dealing both with proof theoretic and model theoretic facts: existence of model completions; amalgamability; Beth definability; interpretability of second order quantifiers and uniform interpolation; definability of dual connectives like difference; and projectivity are among the numerous topics which are covered. Dualities and sheaf representations are the main techniques in the book, together with Ehrenfeucht-Fraisse games and bounded bisimulations. The categorical instruments employed are rich, but a specific extended appendix explains to the reader all concepts used in the text, starting from the very basic definitions to what is needed from topos theory.