Logical Foundations of Mathematics and Com...

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Beschreibung

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.

Zusammenfassung

Presents a wide range of results in logic and computational complexity

Explains the topic informally and then in more detail for the advanced reader

Presents the ideas behind the theoretical concepts

Includes supplementary material: [...]

Inhaltsverzeichnis

¿¿¿¿¿¿¿¿¿¿Mathematician's world.- Language, logic and computations.- Set theory.- Proofs of impossibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.

Details

Erscheinungsjahr:	2013
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	712
Reihe:	Springer Monographs in Mathematics
Inhalt:	xiv 695 S. 45 s/w Illustr. 4 farbige Illustr. 695 p. 49 illus. 4 illus. in color.
ISBN-13:	9783319001180
ISBN-10:	3319001183
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Pudlák, Pavel
Auflage:	2013
Hersteller:	Springer International Publishing Springer International Publishing AG Springer Monographs in Mathematics
Maße:	241 x 160 x 44 mm
Von/Mit:	Pavel Pudlák
Erscheinungsdatum:	31.05.2013
Gewicht:	1,221 kg

preigu-id: 105964841