Background in Logic
Mathematics enables us to model many things abstractly. Group theory, for example, abstracts features of such diverse activities as English changeringing and quantum mechanics. Mathematical logic carries the abstraction one level higher: it is a mathematical model of mathematics. This book shows that the computational complexity of all problems in computer science can be understood via the complexity of their logical descriptions. We begin with a high-level introduction to logic. Although much of the material is well-known, we urge readers to at least skim this background chapter as the concentration on finite and ordered structures, i.e., relational databases, is not standard in most treatments of logic.
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- 1.Usually we will take ϕ0 = true, thus letting |I(A)| = |A|k, cf. Remark 1.32.Google Scholar