Introduction

The book starts with an introduction to categories from a model theoretic perspective. Categorical axiomatizations (Carnap, 1943), categoricity, and functors direct from syntax that were bases for intuitionistic models are the author’s gentle introduction towards topoi characterizations for categorical models and infinite language categories. Nearly all chapters, except for Chapter 2, are recent original areas developed, partly attributed to the author, as a new functorial model theory that reaches to areas on forcing on topos that were only on the author’s abstracts over a decade.