# Logical Foundations of Mathematics and Computational Complexity

## A Gentle Introduction

Part of the Springer Monographs in Mathematics book series (SMM)

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Part of the Springer Monographs in Mathematics book series (SMM)

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. *Logical Foundations of Mathematics and Computational Complexity* covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.

Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs.

*Logical Foundations of Mathematics and Computational Complexity* is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

Complexity of Proofs Computational Complexity Foundations of Mathematics Incompleteness Theorems Mathematical Logic Set-Theoretical Foundations

- DOI https://doi.org/10.1007/978-3-319-00119-7
- Copyright Information Springer International Publishing Switzerland 2013
- Publisher Name Springer, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-00118-0
- Online ISBN 978-3-319-00119-7
- Series Print ISSN 1439-7382
- Buy this book on publisher's site