Akihiro Kanamori: The Higher Infinite

Cover: 9783540888666 | The Higher Infinite | Akihiro Kanamori | Taschenbuch | Paperback

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Beschreibung

The higher in?nite refers to the lofty reaches of the in?nite cardinalities of set t- ory as charted out by large cardinal hypotheses. These hypotheses posit cardinals that prescribe their own transcendence over smaller cardinals and provide a sup- structure for the analysis of strong propositions. As such they are the rightful heirs to the two main legacies of Georg Cantor, founder of set theory: the extension of number into the in?nite and the investigation of de?nable sets of reals. The investigation of large cardinal hypotheses is indeed a mainstream of modern set theory, and they have been found to play a crucial role in the study of de?nable sets of reals, in particular their Lebesgue measurability. Although formulated at various stages in the development of set theory and with different incentives, the hypotheses were found to form a linear hierarchy reaching up to an inconsistent extension of motivating concepts. All known set-theoretic propositions have been gauged in this hierarchy in terms of consistency strength, and the emerging str- ture of implications provides a remarkably rich, detailed and coherent picture of the strongest propositions of mathematics as embedded in set theory. The ?rst of a projected multi-volume series, this text provides a comp- hensive account of the theory of large cardinals from its beginnings through the developments of the early 1970¿s and several of the direct outgrowths leading to the frontiers of current research.

Zusammenfassung

Has become a standard reference and guide in the set theory community

Includes supplementary material: [...]

Inhaltsverzeichnis

Preliminaries.- Beginnings.- Partition Properties.- Forcing and Sets of Reals.- Aspects of Measurability.- Strong Hypotheses.- Determinacy.

Details

Erscheinungsjahr:	2008
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Monographs in Mathematics
Inhalt:	xxii 538 S.
ISBN-13:	9783540888666
ISBN-10:	3540888667
Sprache:	Englisch
Herstellernummer:	12557912
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Kanamori, Akihiro
Auflage:	2nd ed. 2003. Corr. 2nd printing 2005
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Monographs in Mathematics
Maße:	235 x 155 x 30 mm
Von/Mit:	Akihiro Kanamori
Erscheinungsdatum:	28.11.2008
Gewicht:	0,838 kg