Mathematician's world.- Language, logic and computations.- Set theory.- Proofs of impossibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.
"This monograph by the outstanding Czech logician Pavel Pudlak provides a broad but also deep survey of work in logic and computer science relevant to foundational issues, interpreted in a wide sense. ... This is a fine overview of logic and complexity theory that can be confidently recommended to anybody who would like to orient themselves in an increasingly intricate and difficult field." (Alasdair Urquhart, Philosophia Mathematica, Vol. 23 (3), October, 2015)"For the non-expert it offers indeed a 'gentle introduction' to logic that is well selected and excellently explained. And for the logician it certainly offers some of the best introductions to those topics outside their area of direct expertise. ... it contains plenty of informal explanations, intuition and motivation. ... It is truly a gift to the logic and wider communities ... . This book is very enjoyable to read and I wish it all success." (Olaf Beyersdorff, Mathematical Reviews, August, 2014)"It spans the historical, logical, and at times philosophical underpinnings of the theory of computational complexity. Students of mathematics seeking a transition to higher mathematics will find it helpful, as will mathematicians with expertise in other areas. ... an excellent choice for a first text in studying complexity, or as a clarifying adjunct to any assigned text in this area. ... a compact guide for graduate students with a need for or interest in computational complexity and its foundations." (Tom Schulte, MAA Reviews, July, 2014)"This book, exactly as indicated by its title, deals with the main philosophical, historical, logical and mathematical aspects ... in a quite approachable and attractive way. ... the prospective readers of this book are mathematicians with an interest in the foundations, philosophers with a good background in mathematics, and also philosophically minded scientists. Due to the author's nice style, the book will be a very good choice for the first text in studying this subject." (Branislav Boricic, zbMATH, Vol. 1270, 2013)