Difference between revisions of "Cellar"

From Cantor's Attic
Jump to: navigation, search
m (Definition of infinity: added first steps)
 
(9 intermediate revisions by 5 users not shown)
Line 8: Line 8:
 
Meanwhile, we expect that this page and these resources will be expanded as Cantor's attic develops.
 
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 ==  
 
== Elementary set-theoretic topics ==  
  
 +
* [[transitive]]
 +
* [[Ordering Relations|Basic Order Theory]]
 +
* [[ordinal]]
 +
* [[successor ordinal]]
 +
* [[limit ordinal]]
 
* [[cardinality]]
 
* [[cardinality]]
 
* [[axiom of choice]]
 
* [[axiom of choice]]
* [[ZFC]], [[ZF]]
 
 
* [[stationary]], [[club]]
 
* [[stationary]], [[club]]
* [[Hereditary Cardinality]]
+
* [[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 ==  
Line 26: Line 41:
 
* [[Boolean ultrapowers]]
 
* [[Boolean ultrapowers]]
  
 
+
== Canonical inner models ==
== Canonical inner models ==  
+
  
 
* The [[core model]]
 
* The [[core model]]
* The canonical model [[L[mu] | $L[\mu]$]] of one measurable cardinal  
+
* The canonical model [[constructible universe | $L[\mu]$]] of one measurable cardinal  
 
* [[HOD]]
 
* [[HOD]]
* The [[L | constructible universe]]
+
* The [[constructible universe]]
 
+
 
+
 
+
{{stub}}
+

Latest 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.

Definition of infinity

Elementary set-theoretic topics

Axiomatic set theories

Forcing

Canonical inner models