Downward Löwenheim–Skolem theorem
GPTKB entity
Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:first-order_logic
|
| gptkbp:consequence |
first-order theories cannot control the cardinality of their infinite models
|
| gptkbp:field |
gptkb:logic
model theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Downward Löwenheim–Skolem theorem
|
| gptkbp:implies |
gptkb:Skolem's_paradox
|
| gptkbp:namedAfter |
gptkb:Thoralf_Skolem
gptkb:Leopold_Löwenheim |
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Löwenheim–Skolem_theorem
gptkb:Upward_Löwenheim–Skolem_theorem |
| gptkbp:state |
If a first-order theory has an infinite model, then for every infinite cardinal number κ less than or equal to the cardinality of the model, the theory has a model of cardinality κ.
|
| gptkbp:yearProposed |
1915
|
| gptkbp:bfsParent |
gptkb:Gödel–Löwenheim_theorem
|
| gptkbp:bfsLayer |
5
|