upward Löwenheim–Skolem theorem
GPTKB entity
Statements (15)
Predicate | Object |
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gptkbp:instanceOf |
gptkb:mathematical_concept
|
gptkbp:appliesTo |
gptkb:first-order_logic
|
gptkbp:contrastsWith |
categoricity in higher-order logic
|
gptkbp:field |
gptkb:logic
model theory |
https://www.w3.org/2000/01/rdf-schema#label |
upward Löwenheim–Skolem theorem
|
gptkbp:implies |
first-order theories with infinite models have models of all larger infinite cardinalities
|
gptkbp:namedAfter |
gptkb:Thoralf_Skolem
gptkb:Leopold_Löwenheim |
gptkbp:relatedTo |
gptkb:Löwenheim–Skolem_theorem
gptkb:downward_Löwenheim–Skolem_theorem |
gptkbp:state |
If a first-order theory has an infinite model, then for every infinite cardinal number κ greater than or equal to the cardinality of the language, the theory has a model of cardinality κ.
|
gptkbp:yearProposed |
1920s
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gptkbp:bfsParent |
gptkb:Löwenheim–Skolem_theorem
|
gptkbp:bfsLayer |
5
|