This introduction to first-order logic works out the role of first-order logic in the foundations of mathematics, particularly the two fundamental questions of the scope of the axiomatic method and theorem-proving by machines. This is a clear and concise explanation of first-order logic’s role in the foundations of mathematics. It covers several complex subjects not typically covered in basic texts, such as Lindstrom’s theorem on the maximality of first-order logic, Frassé’s characterization of elementary equivalence, and the fundamentals of logic programming.

H.-D. Ebbinghaus, J. Flum, W. Thomas