# Difference between revisions of "Cellar"

From Cantor's Attic

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− | {{DISPLAYTITLE: The | + | {{DISPLAYTITLE: The cellar}} |

This page will contain links to summary accounts of supporting foundational or background material used on the rest of the site. | This page will contain links to summary accounts of supporting foundational or background material used on the rest of the site. | ||

− | + | You may like to begin in the [[playroom]] for an entertaining introduction to infinity. | |

− | * [[ | + | Meanwhile, we expect that this page and these resources will be expanded as Cantor's attic develops. |

− | * [[ | + | |

+ | == Definition of infinity == | ||

+ | |||

+ | * Short informal presentation of the concept of [[infinity]]. | ||

+ | * The [[first steps]] towards infinity. | ||

+ | |||

+ | == Elementary set-theoretic topics == | ||

+ | |||

+ | * [[transitive]] | ||

+ | * [[Ordering Relations|Basic Order Theory]] | ||

+ | * [[ordinal]] | ||

+ | * [[successor ordinal]] | ||

+ | * [[limit ordinal]] | ||

+ | * [[cardinality]] | ||

* [[axiom of choice]] | * [[axiom of choice]] | ||

− | |||

* [[stationary]], [[club]] | * [[stationary]], [[club]] | ||

+ | * [[Hereditary cardinality]] | ||

* [[ultrafilter]], [[measure]] | * [[ultrafilter]], [[measure]] | ||

* [[ultrapower]] | * [[ultrapower]] | ||

+ | * [[Partition property]] | ||

+ | |||

+ | == Axiomatic set theories == | ||

+ | |||

+ | * [[Morse-Kelley set theory]] | ||

+ | * [[ZFC|Zermelo-Fraenkel set theory]] | ||

+ | * [[Positive set theory]] | ||

+ | * [[Kripke-Platek|Kripke-Platek set theory]] | ||

+ | |||

+ | == Forcing == | ||

+ | |||

* [[forcing]] | * [[forcing]] | ||

+ | * [[Boolean-valued models]] | ||

+ | * [[Boolean ultrapowers]] | ||

+ | == Canonical inner models == | ||

− | + | * The [[core model]] | |

+ | * The canonical model [[constructible universe | $L[\mu]$]] of one measurable cardinal | ||

+ | * [[HOD]] | ||

+ | * The [[constructible universe]] |

## Revision as of 09:37, 20 October 2018

This page will contain links to summary accounts of supporting foundational or background material used on the rest of the site.

You may like to begin in the playroom for an entertaining introduction to infinity.

Meanwhile, we expect that this page and these resources will be expanded as Cantor's attic develops.

## Contents

## Definition of infinity

- Short informal presentation of the concept of infinity.
- The first steps towards infinity.

## Elementary set-theoretic topics

- transitive
- Basic Order Theory
- ordinal
- successor ordinal
- limit ordinal
- cardinality
- axiom of choice
- stationary, club
- Hereditary cardinality
- ultrafilter, measure
- ultrapower
- Partition property

## Axiomatic set theories

## Forcing

## Canonical inner models

- The core model
- The canonical model $L[\mu]$ of one measurable cardinal
- HOD
- The constructible universe