International Congress of Mathematicians: Logic, Sets, and Foundations

ICM 2018 - Rio

LOGIC, SETS and FOUNDATIONS

Logic, Sets and Foundations

Computational Complexity

Lambda Calculus with Types

A Modern Approach Sanjeev Arora and Boaz Barak

Henk Barendregt Wil Dekkers and Richard Statman

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

June 2009 253 x 215 mm 594pp 73 b/w illus. 6 tables 307 exercises 978-0-521-42426-4 Hardback £46.99 / US$64.99 P

June 2013 228 x 152 mm 856pp 52 b/w illus. 300 exercises 978-0-521-76614-2 Hardback £65.00 / US$91.00 C

March 2018 228 x 152 mm 284pp 978-1-107-49902-7 Paperback £29.99 / US$39.99 P

Logical Modalities from Aristotle to Carnap

Set Theory

Turing’s Legacy

A First Course Daniel W. Cunningham

Developments from Turing’s Ideas in Logic Edited by Rod Downey

The Story of Necessity Edited by Max Cresswell Edwin Mares and Adriane Rini

Introduces readers to the history of necessity and possibility, two modal concepts which play a key role in philosophy.

September 2016 228 x 152 mm 366pp 978-1-107-07788-1 Hardback £67.99 / US$105.00 C

Perspectives in Logic

Set theory can be considered a unifying theory for mathematics.

This book covers the fundamentals of the subject.

Cambridge Mathematical Textbooks July 2016 228 x 152 mm 262pp 13 b/w illus.

978-1-107-12032-7 Hardback £40.99 / US$60.99 X

The Homotopy Theory of (∞,1) -Categories Julia E. Bergner

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

London Mathematical Society Student Texts, 90

A collection of essays celebrating the influence of Alan Turing’s work in logic, computer science and related areas.

Lecture Notes in Logic, 42 May 2014 228 x 152 mm 539pp 978-1-107-04348-0 Hardback £54.99 / US$76.99 C

The Once and Future Turing Computing the World Edited by S. Barry Cooper and Andrew Hodges

Original essays by world-leading researchers reveal Alan Turing’s lasting contributions to modern research.

March 2016 247 x 174 mm 395pp 49 colour illus. 4 tables 978-1-107-01083-3 Hardback £19.99 / US$31.99 G

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory Martin Grohe

This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.

Lecture Notes in Logic, 47 August 2017 228 x 152 mm 554pp 60 b/w illus.

978-1-107-01452-7 Hardback £120.00 / US$155.00 C

20% discount online at www.cambridge.org/ICM2018

Logic, Sets and Foundations

Why Is There Philosophy of Mathematics At All? Ian Hacking

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

January 2014 216 x 138 mm 304pp 978-1-107-65815-8 Paperback £21.99 / US$29.99 G

Basic Category Theory Tom Leinster

A short introduction ideal for students learning category theory for the first time.

Cambridge Studies in Advanced Mathematics, 143 July 2014 228 x 152 mm 190pp 100 exercises 978-1-107-04424-1 Hardback £38.99 / US$67.00 P

The Computing Universe

Logic Colloquium 2007

Conceptual Mathematics

A Journey through a Revolution Tony Hey and Gyuri Pápay

Edited by Françoise Delon Ulrich Kohlenbach Penelope Maddy and Frank Stephan

This exciting and accessible book takes us on a journey from the early days of computers to the cutting-edge research of the present day.

The 2007 proceedings from the Annual European Meeting of the Association for Symbolic Logic.

A First Introduction to Categories Second edition F. William Lawvere and Stephen H. Schanuel

March 2015 297 x 210 mm 411pp 596 colour illus. 20 tables 978-0-521-15018-7 Paperback £27.00 / US$39.99 G

Lecture Notes in Logic, 35 March 2014 229 x 152 mm 282pp 978-1-107-69677-8 Paperback £27.99 / US$40.99 C

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

July 2009 253 x 177 mm 404pp 575 b/w illus. 12 tables 213 exercises 978-0-521-71916-2 Paperback £39.99 / US$69.99 X

Character Theory and the McKay Conjecture

Analysis of Boolean Functions

Gabriel Navarro

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Tim Roughgarden

June 2014 228 x 152 mm 444pp 13 b/w illus. 450 exercises 978-1-107-03832-5 Hardback £54.99 / US$82.00 P

September 2016 228 x 152 mm 352pp 978-1-316-62479-1 Paperback £24.99 / US$35.99 P

Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

Cambridge Studies in Advanced Mathematics, 175 April 2018 228 x 152 mm 250pp 80 exercises 978-1-108-42844-6 Hardback £47.99 / US$64.99 P

Ryan O’Donnell

Twenty Lectures on Algorithmic Game Theory This accessible introduction features case studies in online advertising, spectrum auctions, kidney exchange, and network management.

20% discount online at www.cambridge.org/ICM2018

Logic, Sets and Foundations

The Logic of Infinity

A Course on Set Theory

The Banach– Tarski Paradox

Barnaby Sheppard

Ernest Schimmerling

This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

This fresh approach to set theory covers the theoretical fundamentals as well as outline connections with other parts of mathematics.

Second edition Grzegorz Tomkowicz and Stan Wagon

July 2014 247 x 174 mm 498pp 45 b/w illus.

978-1-107-67866-8 Paperback £29.99 / US$46.99 P

July 2011 228 x 152 mm 178pp 10 b/w illus. 100 exercises 978-1-107-40048-1 Paperback £30.99 / US$51.99 P

Tame Topology and O-minimal Structures

Elements of Logical Reasoning

L. P. D. van den Dries

This book provides an accessible and at the same time scientifically rigorous introduction to the principles of logical reasoning.

These notes give a self-contained treatment of the theory of o-minimal structures.

London Mathematical Society Lecture Note Series, 248 May 1998 228 x 152 mm 192pp 978-0-521-59838-5 Paperback £52.99 / US$81.99 C

Jan von Plato

January 2014 247 x 174 mm 271pp 978-1-107-61077-4 Paperback £16.99 / US$24.99 P

The Banach–Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.

Alan M. Turing Centenary Edition Sara Turing Foreword by Martin Davis and Lyn Irvine Afterword by John Turing

Encyclopedia of Mathematics and its Applications, 163

Containing never-beforepublished material, this fascinating account sheds new light on one of the greatest figures of the twentieth century.

October 2016 234 x 156 mm 360pp 47 b/w illus. 6 colour illus.

978-1-107-04259-9 Hardback £74.99 / US$110.00 P

November 2014 216 x 140 mm 194pp 7 b/w illus.

978-1-107-52422-4 Paperback £9.99 / US$15.99 G

Proof Analysis

Structural Proof Theory

A Contribution to Hilbert’s Last Problem Sara Negri and Jan von Plato

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

June 2014 244 x 170 mm 278pp 978-1-107-41723-6 Paperback £31.99 / US$46.99 C

Sara Negri and Jan von Plato Appendix by Aarne Ranta

A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.

July 2008 228 x 152 mm 276pp 978-0-521-06842-0 Paperback £31.99 / US$46.99 C

20% discount online at www.cambridge.org/ICM2018