The Logic of Provability

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McGee, Vann 1994. On the degrees of unsolvability of modal predicate logics of provability. Journal of Symbolic Logic, Vol. 59, Issue. 1, p. 253.

CrossRef

Google Scholar

Governatori, Guido 1996. Practical Reasoning. Vol. 1085, Issue. , p. 291.

CrossRef

Google Scholar

LINDSTRöM, PER 1996. Provability logic—a short introduction. Theoria, Vol. 62, Issue. 1-2, p. 19.

CrossRef

Google Scholar

Dowek, Gilles 1998. Types for Proofs and Programs. Vol. 1512, Issue. , p. 88.

CrossRef

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Demri, Stéephane and Goré, Rajeev 1999. Automated Deduction — CADE-16. Vol. 1632, Issue. , p. 16.

CrossRef

Google Scholar

Demri, Stéphane and Goré, Rajeev 2000. Automated Deduction in Classical and Non-Classical Logics. Vol. 1761, Issue. , p. 152.

CrossRef

Google Scholar

Ehrig, Hartmut Mahr, Bernd Große-Rhode, Martin Cornlius, Felix and Zeitz, Philip 2001. Mathematisch-strukturelle Grundlagen der Informatik. p. 401.

CrossRef

Google Scholar

Nakano, Hiroshi 2001. Theoretical Aspects of Computer Software. Vol. 2215, Issue. , p. 165.

CrossRef

Google Scholar

Švejdar, Vítězslav 2003. The decision problem of provability logic with only one atom. Archive for Mathematical Logic, Vol. 42, Issue. 8, p. 763.

CrossRef

Google Scholar

Jeřábek, Emil 2004. A note on Grzegorczyk's logic. Mathematical Logic Quarterly, Vol. 50, Issue. 3, p. 295.

CrossRef

Google Scholar

Serény, György 2004. Boolos‐style proofs of limitative theorems. Mathematical Logic Quarterly, Vol. 50, Issue. 2, p. 211.

CrossRef

Google Scholar

Joosten, Joost J. 2005. The Closed Fragment of the Interpretability Logic of PRA with a Constant for $\mathrm{I}\Sigma_1$. Notre Dame Journal of Formal Logic, Vol. 46, Issue. 2,

CrossRef

Google Scholar

Macintyre, Angus 2005. The mathematical significance of proof theory. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 363, Issue. 1835, p. 2419.

CrossRef

Google Scholar

Brandenburger, Adam and Keisler, H. Jerome 2006. An Impossibility Theorem on Beliefs in Games. Studia Logica, Vol. 84, Issue. 2, p. 211.

CrossRef

Google Scholar

Goris, Evan 2006. Interpolation and the Interpretability Logic of PA. Notre Dame Journal of Formal Logic, Vol. 47, Issue. 2,

CrossRef

Google Scholar

Humberstone, Lloyd 2006. Variations on a Theme of Curry. Notre Dame Journal of Formal Logic, Vol. 47, Issue. 1,

CrossRef

Google Scholar

Lindström, Per 2006. Note on Some Fixed Point Constructions in Provability Logic. Journal of Philosophical Logic, Vol. 35, Issue. 3, p. 225.

CrossRef

Google Scholar

Visser, Albert and Jonge, Maartje de 2006. No Escape from Vardanyan's theorem. Archive for Mathematical Logic, Vol. 45, Issue. 5, p. 539.

CrossRef

Google Scholar

Artemov, Sergei 2007. Mathematical Problems from Applied Logic II. Vol. 5, Issue. , p. 1.

CrossRef

Google Scholar

Kahle, Reinhard 2007. Die Gödelschen Unvollständigkeitssätze . Mathematische Semesterberichte, Vol. 54, Issue. 1, p. 1.

CrossRef

Google Scholar

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George S. Boolos, Massachusetts Institute of Technology

Publisher:: Cambridge University Press
Online publication date:: January 2010
Print publication year:: 1994
Online ISBN:: 9780511625183
DOI:: https://doi.org/10.1017/CBO9780511625183

Subjects:: Mathematics (general), Mathematics, Logic, Philosophy

30.99 (GBP)

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The Logic of Provability
George S. Boolos
Online ISBN: 9780511625183

Book DOI: https://doi.org/10.1017/CBO9780511625183
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This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.

"The book contains an excellent combination of values: noble subject, fresh key results, and the gentle, friendly style of the author. It can be recommended as a textbook, as a handbook, or simply as high quality reading in logic." Sergei N. Artemov, Journal of Symbolic Logic

"I found it lively, lucid, and informative...Boolos' style of writing is unusually kind to the reader. When an argument becomes tricky, he breaks it down into a lot of small steps, showing the reader in detail just how to proceed. A result is that the book is remarkably easy to read." Vann McGee, Rutgers University

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The Logic of Provability

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xiv

Introduction
pp xv-xxxvi

1 - GL and other systems of propositional modal logic
pp 1-14

2 - Peano arithmetic
pp 15-50

3 - The box as Bew(x)
pp 51-67

4 - Semantics for GL and other modal logics
pp 68-77

5 - Completeness and decidability of GL and K, K4, T, B, S4, and S5
pp 78-84

6 - Canonical models
pp 85-91

7 - On GL
pp 92-103

8 - The fixed point theorem
pp 104-123

9 - The arithmetical completeness theorems for GL and GLS
pp 124-137

10 - Trees for GL
pp 138-147

11 - An incomplete system of modal logic
pp 148-154

12 - An S4-preserving proof-theoretical treatment of modality
pp 155-164

13 - Modal logic within set theory
pp 165-176

14 - Modal logic within analysis
pp 177-186

15 - The joint provability logic of consistency and ω-consistency
pp 187-207

16 - On GLB: The fixed point theorem, letterless sentences, and analysis
pp 208-218

17 - Quantified provability logic
pp 219-241

18 - Quantified provability logic with one one-place predicate letter
pp 242-255

Notes
pp 256-261

Bibliography
pp 262-270

Index
pp 271-275

Notation and symbols
pp 276-276

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The Logic of Provability

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