Lectures on Mathematical Logic, Volume II

This volume is a combinatorial study of derivations and deductions. The author's approach is syntactical and builds from Gentzen's basic ideas into logical rules and a calculus of deductive situations. The book concludes with the algorithms producing the results of Gentzen's midsequent theorem and Herbrand's theorem for prenex formulas.

In this volume, logic starts from the observation that in everyday arguments, as brought forward by say a lawyer, statements are transformed linguistically, connecting them in formal ways irrespective of their contents. Understanding such arguments as deductive situations, or "sequents" in the technical terminology, the transformations between them can be expressed as logical rules. The book concludes with the algorithms producing the results of Gentzen's midsequent theorem and Herbrand's theorem for prenex formulas.