The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (Perspectives in Mathematical Logic) - Hardcover

Kanamori, Akihiro

Hardcover

ISBN 10: 3540570713 ISBN 13: 9783540570714

Publisher: Springer, 1997

Synopsis

After describing the beginnings of the subject - the theory of large cardinals - a comprehensive account is given of the work in the 1960s on partition properties, forcing and sets of reals, and aspects of measurability (including saturated ideals and inner models of measurability). Then discussed are the strong hypotheses like supercompactness up to Kunen's inconsistency. The last sections describe the investigation of determinacy from its beginnings up to a survey of the recent consistency results of Woodin. The material is presented in the context of its historical development and leads to the frontiers of contemporary research. It will serve as a reference and guide to graduate students and researchers in set theory and set-theoretic topology.

About this title

Review:

"The exposition is intelligent and well-paced; ...as a source book it is a compendium of references, well indexed, and it will become literally the reference book, a Baedeker, for the enquiring student of the subject. It should therefore be on every University Librarys mathematical shelf." Proceedings of the Edinburgh Mathematical Society

"The exposition is intelligent and well-paced;...as a source book it is a compendium of references, well indexed, and it will become literally the reference book, a Baedeker, for the enquiring student of the subject. It should therefore be on every University Librarys mathematical shelf." Proceedings of the Edinburgh Mathematical Society

From the Back Cover:

The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contempory research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterpreise but also become prepared to pursue research in several specific areas by studying the relevant sections.

About this edition

• Publisher: Springer
• Publication date: 1997
• ISBN 10: 3540570713
• ISBN 13: 9783540570714
• Binding: Hardcover
• Edition number: 1
• Number of pages: 536