# Difference between revisions of "Cellar"

From Cantor's Attic

BartekChom (Talk | contribs) |
|||

(20 intermediate revisions by 8 users not shown) | |||

Line 1: | Line 1: | ||

− | {{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]] |

+ | * [[model]] | ||

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

+ | |||

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

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

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

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

+ | * [[New Foundations]] | ||

+ | |||

+ | == Forcing == | ||

+ | |||

+ | * [[forcing]] | ||

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

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

− | + | [[Category:The cellar]] |

## Latest revision as of 22:38, 21 August 2021

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
- model

## Axiomatic set theories

- Morse-Kelley set theory
- Zermelo-Fraenkel set theory
- Positive set theory
- Kripke-Platek set theory
- New Foundations