The Higher Infinite.: Large Cardinals in Set Theory from their Beginnings (Perspectives in Mathematical Logic) - Tapa dura

"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

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.