Proof Analysis: A Contribution to Hilbert's Last Problem

ISBN-13: 9781107008953 / Angielski / Twarda / 2011 / 265 str.

Sara Negri

Opis

Presents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic.

Recenzje

"...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

Spis treści

Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; Part IV. Proof Systems for Nonclassical Logics: 11. Modal logic; 12. Quantified modal logic, provability logic, and so on; Bibliography; Index of names; Index of subjects.