PP-2006-22:
Kieftenbeld, Vincent
(2006)
*Notions of Strong Compactness without the Axiom of Choice.*
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## Abstract

The study of large cardinal axioms is an active part of contemporary

set theory. For a large cardinal notion there are often several

definitions possible. For example, two common ways to define a large

cardinal notion is as a critical point of an elementary embedding with

certain properties, or in terms of ultrafilters. Many other types of

definitions exist. With the axiom of choice these definitions are

often equivalent. Without the axiom of choice, these definitions may

not be equivalent anymore. Moreover the consistency strength of the

large cardinal axiom may change with the ambient set theory, depending

on which definition you choose. In this thesis we study several

different definitions related to the notion of a compact cardinal. We

will be guided by two main questions: What is the structure of

implications between different definitions? And: What is the relative

consistency strength of these definitions? In both cases the answers

may depend on the presence or absence of the axiom of choice.

Item Type: | Report |
---|---|

Report Nr: | PP-2006-22 |

Series Name: | Prepublication (PP) Series |

Year: | 2006 |

Uncontrolled Keywords: | strongly compact cardinals; axiom of choice; elementary embedding; infinitary language |

Subjects: | Language |

Depositing User: | Benedikt |

Date Deposited: | 12 Oct 2016 14:36 |

Last Modified: | 12 Oct 2016 14:36 |

URI: | https://eprints.illc.uva.nl/id/eprint/197 |

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