Proof Analysis: A Contribution to Hilbert’s Last Problem 1st Edition by Sara Negri (PDF)

Description

This book continues from where the authors’ previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

User’s Reviews

Editorial Reviews: Review “…provide a substantial contribution to the development of proof theory in mathematics…. The book covers a lot of useful material in a concise, efficient and very clearly structured manner. The chapters are written with a palpable intention to show how vast the applicability of the methods is. The results are uniform, general and require a high-level preparation in many different fields. This book can be seen as the stimulating continuation of the authors’ introductory book Structural Proof Theory…” –F. Poggiolesi, Institut d’Histoire et Philosophie des Sciences, Paris, France, History and Philosophy of Logic Book Description Presents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic. About the Author Sara Negri is Docent of Logic at the University of Helsinki. She is the author of Structural Proof Theory (Cambridge University Press, 2001, with Jan von Plato) and she has also written several research papers on mathematical and philosophical logic.Jan von Plato is Professor of Philosophy at the University of Helsinki. He is the author of Creating Modern Probability (Cambridge University Press, 1994), the co-author (with Sara Negri) of Structural Proof Theory (Cambridge University Press, 2001) and has written several papers on logic and epistemology. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is the sequence of Structural Proof Theory. Besides that, the objective consists in giving a thorough understanding of how to treat axioms from mathematical theories into proof theory either with sequent calculus or natural deduction. This is an excellent complementary book to the first, being as detailed and good as Structural Proof Theory is in developing the metamathematics of Gentzen systems.

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