Basic proof theory

"This introduction to the basic ideas of structural proof theory contains a through discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic." "In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous…