Course of Mathematical Logic. Volume 2: Model Theory

✍ Scribed by Roland Fraïssé

• Publisher: Springer
• Year: 1974
• Tongue: English
• Leaves: 215
• Series: Synthese Library 69
• Category: Library

✦ Synopsis

This book is addressed primarily to researchers specializing in mathemat­ ical logic. It may also be of interest to students completing a Masters Degree in mathematics and desiring to embark on research in logic, as well as to teachers at universities and high schools, mathematicians in general, or philosophers wishing to gain a more rigorous conception of deductive reasoning. The material stems from lectures read from 1962 to 1968 at the Faculte des Sciences de Paris and since 1969 at the Universities of Provence and Paris-VI. The only prerequisites demanded of the reader are elementary combinatorial theory and set theory. We lay emphasis on the semantic aspect of logic rather than on syntax; in other words, we are concerned with the connection between formulas and the multirelations, or models, which satisfy them. In this context considerable importance attaches to the theory of relations, which yields a novel approach and algebraization of many concepts of logic. The present two-volume edition considerably widens the scope of the original [French] one-volume edition (1967: Relation, Formule logique, Compacite, Completude). The new Volume 1 (1971: Relation et Formule logique) reproduces the old Chapters 1, 2, 3, 4, 5 and 8, redivided as follows: Word, formula (Chapter 1), Connection (Chapter 2), Relation, operator (Chapter 3), Free formula (Chapter 4), Logicalformula,denumer­ able-model theorem (L6wenheim-Skolem) (Chapter 5), Completeness theorem (G6del-Herbrand) and Interpolation theorem (Craig-Lyndon) (Chapter 6), Interpretability of relations (Chapter 7).

✦ Table of Contents

Front Matter....Pages I-XIX
Local Isomorphism and Logical Formula; Logical Restriction Theorem....Pages 1-29
Logical Convergence; Compactness, Omission and Interpretability Theorems....Pages 30-45
Elimination of Quantifiers....Pages 46-69
Extension Theorems....Pages 70-92
Theories and Axiom Systems....Pages 93-111
Pseudo-Logical Class; Interpretability of Theories; Expansion of a Theory; Axiomatizability....Pages 112-126
Ultraproduct....Pages 127-143
Forcing....Pages 144-157
Isomorphisms and Equivalences in Relation to the Calculus of Infinitely Long Formulas with Finite Quantifiers....Pages 158-178
Back Matter....Pages 179-197

✦ Subjects

Logic; Mathematical Logic and Foundations