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Beschreibung
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively… independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
07.12.2013
Sprache
Englisch
EAN
9781461488538
Herausgeber
Springer US
Sonderedition
Nein
Autor
Abhijit Dasgupta
Seitenanzahl
444
Einbandart
Gebundene Ausgabe
Buch Untertitel
With an Introduction to Real Point Sets
Schlagwörter
Cantor's Theorem, Dedekind's Theorem, Frege, Zermelo-Fraenkel axiom system, order, cardinals, and ordinals, set theory, mathematical logic
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
PBK - Mathematische Analysis, allgemein
PBF - Algebra
PBP - Topologie
PBD - Diskrete Mathematik
QDTL - Philosophie: Logik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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