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Paolo Mancosu, Sergio Galvan, Richard Zach: An Introduction to Proof Theory (Paperback, Oxford University Press) 3 stars

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with …

Wordy

3 stars

Hard to tell. The book is accessible, but maybe too accessible; verbose. It literally starts with high-school-level induction, and devotes 50 pages to axiomatic calculi just to show that how difficult it is to work with. While more clearly presented, it used approximately 250 pages for what Negri and Plato's book presented with around 80 pages. Meanwhile it is self-contained; it even devoted an entire chapter to ordinal notations and transfinite inductions, which should be covered in set theory texts, and also contains quite some valuable and cleanly organized historical motivations.

In the preface the authors stated that the book is especially for those in philosophy who have only a minimal background in mathematics and logic. For those with relevant background the book is largely a waste of time. Troelstra & Schwichtenberg's Basic Proof Theory is the way to go.