Bounded Variable Logics and Counting A Study in Finite Models [Hardcover]

This study introduces some central ideas and lines of research in finite model theory, particularly bounded variable infinitary logics.This study introduces some central ideas and lines of research in finite model theory - particularly bounded variable infinitary logics - and explores the fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory.This study introduces some central ideas and lines of research in finite model theory - particularly bounded variable infinitary logics - and explores the fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory.Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the ninth publication in the Lecture Notes in Logic series, Martin Otto gives an introduction to finite model theory that indicates the main ideas and lines of inquiry that motivate research in this area. Particular attention is paid to bounded variable infinitary logics, with and without counting quantifiers, related fixed-point logics, and the corresponding fragments of Ptime. The relations with Ptime exhibit the fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory.Preface; Introduction; 1. Definitions and preliminaries; 2. The games and their analysis; 3. The invariants; 4. Fixed-point logic with counting; 5. Related Lindstr?m extensions; 6. Canonization problems; 7. Canonization for two variables; Bibliography; Index.