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CHAPTER 2. FIRST ORDER LOGIC
1. Introduction First order logic is a much richer system than sentential logic. Its interpre- tations include the usual structures of mathematics, and its sentences enable us to express many properties of these structures. For example, consider the following English sentence: Everything greater than 0 has a square root. This can be interpreted, for example, in arithmetic on Q, the set of rational numbers, where it is false, and in arithmetic on R, the set of real numbers, where it is true. How could we express this in a formal language? The following is at least a first approximation. For all x (0