ISBN : 9780198790402
Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike. It is written with an eye towards accessibility: the only prerequisite is any introductory logic course, and definitions and concepts are built-up incrementally as the book proceeds, with shorter proofs given in the body of the text and longer proofs relegated to the appendices of the chapters.
A: Reference and realism; 1 Logics and languages; 2 Permutations and referential indeterminacy; 3 Ramsey sentences and Newman's objection; 4 Compactness, infinitesimals, and the reals; 5 Sameness of structure and theory; B: Categoricity; 6 Modelism and mathematical doxology; 7 Categoricity and the natural numbers; 8 Categoricity and the sets; 9 Transcendental arguments; 10 Internal categoricity and the natural numbers; 11 Internal categoricity and the sets; 12 Internal categoricity and truth; 13 Boolean-valued structures; C: Indiscernibility and classification; 14 Types and Stone spaces; 15 Indiscernibility; 16 Quantifiers; 17 Classification and uncountable categoricity; D: Historical appendix; Wilfrid Hodges: A short history of model theory