By Michael Makkai
Utilizing the idea of different types as a framework, this ebook develops a duality conception for theories in first order common sense within which the twin of a idea is the class of its types with appropriate extra constitution. This duality conception resembles and generalizes M. H. Stone's recognized duality idea for Boolean algebras. As an software, Makkai derives a end result such as the well known definability theorem of E. W. Beth. This new definability theorem is expounded to theorems of descent in class idea and algebra and will even be acknowledged consequently in natural good judgment irrespective of class concept. Containing novel thoughts in addition to purposes of classical tools, this conscientiously written booklet indicates awareness to either association and aspect and should attract mathematicians and philosophers drawn to type thought.