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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Grundlagen Introduction to Incompleteness
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Introduction to Incompleteness
Serafim Batzoglou (Gebundene Ausgabe, Englisch)
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Beschreibung
Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aims to help bridge this pedagogical gap by providing a complete and accessible technical exposition of… incompleteness for a wide audience. The author accomplishes this by making conceptually difficult proofs more approachable by providing intuitive explanations of the main ideas. Care is taken to emphasize the different layers of the mathematical argument – the layer within and the metalayer about an axiomatic system. Structurally, the book efficiently examines key results and arrives at some of the most interesting concepts as quickly as possible. It begins with Gödel's incompleteness theorems before continuing on to challenging concepts in the arithmetized completeness theorem, the Paris-Harrington theorem, and the independence of the continuum hypothesis. Other topics covered include the Lucas-Penrose arguments, ordinals and cardinals, and axiomatic set theory. Additionally, the author’s coverage of forcing is a notable addition to the existing literature. Introduction to Incompleteness will be of interest to researchers, students, and instructors looking for a resource to teach this topic. It may also be suitable for self-study. Knowledge of undergraduate-level theoretical mathematics or computer science is required, as well as a familiarity with abstract proofs. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
31.08.2024
Sprache
Englisch
EAN
9783031642166
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Serafim Batzoglou
Seitenanzahl
302
Einbandart
Gebundene Ausgabe
Buch Untertitel
From Gödel's Theorems to Forcing and the Continuum Hypothesis
Schlagwörter
Kurt Gödel, Gödel incompleteness theorems, Gödel completeness theorems, Mathematical incompleteness, Continuum hypothesis, Peano Arithmetic, Recursive functions, Compactness theorems, Lucas-Penrose arguments, CH-forcing, Mathematical independence, Paris-Harrington theorem, Ramsey theory
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
PBCH - Mengenlehre
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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