Review by Choice Review
As proof constitutes the universal characteristic modality of research mathematics and the heart of its daily practice, it may seem odd that the subject known as proof theory remains outside the ken even of many mathematical logicians. The famous incompleteness theory of Godel precludes any proof of the consistency of arithmetic that is formalizable within arithmetic. But surprisingly, the core of proof theory forms around the quest for such consistency proofs, albeit necessarily unformalizable, but nevertheless sufficiently mechanical to advance just the same formalist program that most mathematicians presume demolished by Godel's work . That proof theory remains poorly known owes to the difficulty of articulating its subtle goals, its technical dependence on advanced theory of the ordinals, and a lack of broadly aimed expositions. This work by Pohlers (Westfalische Wilhelms-Universitat Munster, Germany), originally planned as a second edition of the author's Proof Theory: An Introduction (1989), promises to speak to a wider audience, but disappoints. Linguistic infelicities and typos amid great technicalities come as annoyances. Most importantly, the subject calls for a better instinct concerning what to, and what not to, spell out to bring in readers from outside the specialty. The intrepid can certainly learn here, but the subject still wants for a gracious articulation. Summing Up: Optional. Upper-division undergraduates through professionals. D. V. Feldman University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
