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.
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