Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas

Gebundenes Buch

Mathematical Logic

Beschreibung

This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: 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 Goedel's work: 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.

Produktdetails

• Undergraduate Texts in Mathematics
• Verlag: Springer, Berlin
• 2nd ed. repr.
• Seitenzahl: 289
• Englisch
• Abmessung: 245mm
• Gewicht: 622g
• ISBN-13: 9783540942580
• Artikelnr.: 27973831

Rezensionen

"This newest edition has been reclassified, fittingly, as a graduate text, and it is admirably suited to that role. ... Those who are already well-versed in logic will find this text to be a valuable reference and a strong resource for teaching at the graduate level, while those who are new to the field will come to know not only how mathematical logic is studied but also, perhaps more importantly, why." (Stephen Walk, MAA Reviews, January 6, 2023)