@book {MATHEDUC.05834200,
author = {Hoffmann, Dirk W.},
title = {Limits of mathematics. A journey through the core subjects of mathematical logic. (Grenzen der Mathematik. Eine Reise durch die Kerngebiete der mathematischen Logik.)},
year = {2011},
isbn = {978-3-8274-2559-1},
pages = {ix, 409~p.},
publisher = {Heidelberg: Spektrum Akademischer Verlag},
doi = {10.1007/978-3-8274-2560-7},
abstract = {This is an unusually ambitious book, as it aims to present -- at times with complete proofs! -- some of the 20th century most impressive results in logic to a wider audience. Starting with Cantor's set-theoretical revolution, the author moves to formal systems in first-order logic, Peano arithmetic, ZF set theory, G\"odel's incompleteness theorems (with proofs!), a presentation of Goodstein's theorem as an example of a true but PA-unprovable sentence, recursion theory (with Diophantine representation and Hilbert's Tenth Problem), algorithmic information theory (with Chaitin's incompleteness theorem), and model theory. The book is filled with graphical means of conveying in a lively manner the abstract notions, comments on the material, warnings of false interpretations, and can be said to be written with the reader in mind at every page. It is hard for the reviewer to judge whether the intended audience (such as bright high school students) can read this book and absorb the wealth of information presented, but the effort that went into having even attempted it is certainly commendable.},
reviewer = {Victor V. Pambuccian (Dortmund)},
msc2010 = {E30xx},
identifier = {2013b.00473},
}