Author | Kanamori, Akihiro. author |
---|---|

Title | The Higher Infinite [electronic resource] : Large Cardinals in Set Theory from Their Beginnings / by Akihiro Kanamori |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |

Edition | 2 |

Connect to | http://dx.doi.org/10.1007/978-3-540-88867-3 |

Descript | XXII, 538 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Mathematical logic
Topology
Mathematics
Mathematical Logic and Foundations
Topology