Difference between revisions of "Cellar"
From Cantor's Attic
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{{DISPLAYTITLE: The cellar}} | {{DISPLAYTITLE: The cellar}} | ||
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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. | ||
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You may like to begin in the [[playroom]] for an entertaining introduction to infinity. | You may like to begin in the [[playroom]] for an entertaining introduction to infinity. | ||
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== Definition of infinity == | == Definition of infinity == | ||
| − | * Short informal presentation of the concept of [[infinity]] | + | * Short informal presentation of the concept of [[infinity]]. |
| + | * The [[first steps]] towards infinity. | ||
== Elementary set-theoretic topics == | == Elementary set-theoretic topics == | ||
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* [[ultrafilter]], [[measure]] | * [[ultrafilter]], [[measure]] | ||
* [[ultrapower]] | * [[ultrapower]] | ||
| + | * [[Partition property]] | ||
| + | * [[model]] | ||
== Axiomatic set theories == | == Axiomatic set theories == | ||
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* [[ZFC|Zermelo-Fraenkel set theory]] | * [[ZFC|Zermelo-Fraenkel set theory]] | ||
* [[Positive set theory]] | * [[Positive set theory]] | ||
| − | * [[ | + | * [[Kripke-Platek|Kripke-Platek set theory]] |
| + | * [[New Foundations]] | ||
== Forcing == | == Forcing == | ||
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* [[Boolean ultrapowers]] | * [[Boolean ultrapowers]] | ||
| − | + | [[Category:The cellar]] | |
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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
