Mathematical logic

Graduate Texts in Mathematics #291

by Heinz-Dieter Ebbinghaus

This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of What is a proof How can a proof be justified To what extent can a proof be made a purely mechanical procedure How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedells First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraisse's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

Genres: Mathematics, Logic

289 pages, Hardcover

First published January 1, 1978

Reviews

[Nick]

The second part of this book contains a useful introduction to the foundations of logic programming, such as Herbrand semantics.