Introduction to Mathematical Logic

This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it. The book is meant primarily for mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculus. Today we know of many calculi which have this property.

Autorentext
Diana Schmidt, Frühpädagogin B.A., geb. 1986 in München, absolvierte nach ihrer Ausbildung zur Sozialassistentin und Erzieherin das Bachelorstudium Integrative Frühpädagogik. Zurzeit studiert sie im Masterstudium Soziale Kohäsion. Im Rahmen des Studiums forscht die Autorin zu den Themen sexueller Kindesmissbrauch und aktuell zum Thema Resilienzförderung in Krippen. Durch zahlreiche Praktika in unterschiedlichen pädagogischen Einrichtungen, darunter ein Auslandspraktikum, sammelte sie umfangreiche Erfahrungen in der Elementarpädagogik. Ihre Schwerpunkte liegen im Bereich der Vorbeugung und Auseinandersetzung von und mit psychischen Störungen bei Kleinkindern.

Inhalt
I. Introduction.- II. The Language of Predicate Logic.- III. The Semantics of Predicate Logic.- IV. A Predicate Calculus.- V. Gödel's Completeness Theorem.- VI. Peano's Axiom System.- VII. Extensions of the Language, Normal Forms.- VIII. The Theorems of A. Robinson, Craig and Beth.- IX. Miscellaneous.- Further Reading.- Index of Abbreviations for Defining and Derived Rules.- Notation.- Name and Subject Index.