Models and Ultraproducts An Introduction

The study of the relationship between formal languages and abstract structures, model theory covers a very wide field. This text focuses on the ultraproduct construction and those areas in which it is useful. Geared toward advanced undergraduates and graduate students, it assumes only an acquaintance with the rudiments of set theory. Topics include the work of Jonsson and of Morley and Vaught on homogeneous universal models, the results of Keisler in connection with the notion of a saturated structure, classical results of Godel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text. 1974 ed.

John L. Bell is a Professor of Philosophy at the University of Western Ontario and Alan Slomson is Director of Undergraduate Studies at the University of Leeds' School of Mathematics.