Mathematical logic

New York: Springer. Edited by Jörg Flum & Wolfgang Thomas (1996)
  Copy   BIBTEX

Abstract

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. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A course in mathematical logic.J. L. Bell - 1977 - New York: sole distributors for the U.S.A. and Canada American Elsevier Pub. Co.. Edited by Moshé Machover.
The elements of mathematical logic.Paul Charles Rosenbloom - 1950 - New York]: Dover Publications.
Mathematical logic.Stephen Cole Kleene - 1967 - Mineola, N.Y.: Dover Publications.
First order mathematical logic.Angelo Margaris - 1967 - New York: Dover Publications.
Modern logic: a text in elementary symbolic logic.Graeme Forbes - 1994 - New York: Oxford University Press.
Notes on logic and set theory.P. T. Johnstone - 1987 - New York: Cambridge University Press.
Reductive logic and proof-search: proof theory, semantics, and control.David J. Pym - 2004 - New York: Oxford University Press. Edited by Eike Ritter.

Analytics

Added to PP
2009-01-28

Downloads
35 (#395,891)

6 months
4 (#319,344)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A new solution to the paradoxes of rational acceptability.Igor Douven - 2002 - British Journal for the Philosophy of Science 53 (3):391-410.
Can robots make good models of biological behaviour?Barbara Webb - 2001 - Behavioral and Brain Sciences 24 (6):1033-1050.
The preface paradox revisited.Igor Douven - 2003 - Erkenntnis 59 (3):389 - 420.
Indiscernibles, general covariance, and other symmetries.Simon Saunders - 2001 - In Abhay Ashtekar, Jürgen Renn, Don Howard, Abner Shimony & S. Sarkar (eds.), Revisiting the Foundations of Relativistic Physics. Festschrift in Honour of John Stachel. Kluwer Academic Publishers.

View all 41 citations / Add more citations

References found in this work

No references found.

Add more references