Introduction to Cardinal Arithmetic

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Sprache: Englisch

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Beschreibung

This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.

Zusammenfassung

Self-contained introduction to cardinal arithmetic which also includes pcf theory

Gives a relatively complete survey of results provable in ZFC

Includes supplementary material: [...]

Inhaltsverzeichnis

Foundations.- The Galvin-Hajnal Theorem.- Ordinal Functions.- Approximation Sequences.- Generators of T +(a).- The Supremum of pcf ? (a).- Local Properties.- Applications of pcf-Theory.- The Cardinal Function pp(?).

Details

Erscheinungsjahr:	2009
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Reihe:	Modern Birkhäuser Classics
Inhalt:	vii 304 S.
ISBN-13:	9783034603270
ISBN-10:	3034603274
Sprache:	Englisch
Herstellernummer:	12779284
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Holz, Michael Weitz, E. Steffens, Karsten
Auflage:	1st ed.1999. 2nd printing 2009
Hersteller:	Birkhäuser Basel Springer Basel AG Modern Birkhäuser Classics
Maße:	244 x 170 x 18 mm
Von/Mit:	Michael Holz (u. a.)
Erscheinungsdatum:	23.11.2009
Gewicht:	0,548 kg