We present a basic axiomatic development of Zermelo-Fraenkel and Choice set theory, commonly abbreviated ZFC. This paper is aimed in particular at students of mathematics who are familiar with set theory from a “naive” perspective, and are interested in the underlying axiomatic development. We will quickly review some basic concepts of set theory, before focusing on the set theoretic definition...

Institution theory represents the fully axiomatic approach to model in which all components of logical systems are treated abstractly by reliance on category theory. Here, we survey some developments over last decade or so concerning institution theoretic non-classical aspects Our focus will be many-valued truth and models with states, addressed two extensions ordinary known as L-institutions s...

Rational conformal field theories are reviewed from an (informal) axiomatic stand point. This approach sheds new light on the classification of conformal current algebra models. On the other hand, the study of 2D CFT gives rise to new questions in the general theory. We display as an example embeddings of local chiral algebras which are not of the Doplicher–Haag–Roberts type. The interrelation ...