Basic Formal Concepts and Terminology

This chapter is devoted to, on the one hand, a brief presentation of the standard logical and mathematical terminology and theory which will be frequently used in the rest of this book, and on the other, to proofs of some results within elementary set theory and algebra which will be used in later chapters. It is intended to function mainly as a kind of “dictionary” which the reader can consult when necessary. Section 2.1 and the beginning of sections 2.7 and 2.9 contain the basic apparatus for Part 2 and should therefore be at least cursorily perused before proceeding further. But the remaining sections can wait until they are referred to. Even though most terms which will be used are defined, a familiarity with elementary set theory and logic as presented in for example Suppes (1957) or Stoll (1963) is presupposed.