Titlebook: Logical Foundations of Mathematics and Computational Complexity; A Gentle Introductio Pavel Pudlák Book 2013 Springer International Publish

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1439-7382 e 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 and978-3-319-34268-9978-3-319-00119-7Series ISSN 1439-7382 Series E-ISSN 2196-9922

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Language, Logic and Computations,e show how proofs, the main product of mathematical research, are formalized. We also present the main concepts of the theory of computations. Finally, we consider an important formal system, the .-calculus, which can be used to formalize logical reasoning and computations at the same time.

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Consistency, Truth and Existence,hermore, we present some results of the program of using large cardinals to cope with incompleteness in set theory. In the final section, we present the concept of physical natural numbers and attempt to give an alternative formalization of this concept.

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1439-7382 d reader.Presents the ideas behind the theoretical concepts..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

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The Complexity of Computations,r factoring integers. The topic of the last section is important for the foundations of mathematics, although it is less related to computational complexity; it is about algorithmic complexity of finite strings of bits.

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