upward Löwenheim–Skolem theorem

GPTKB entity

Statements (15)
Predicate Object
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
gptkbp:bfsParent gptkb:Löwenheim–Skolem_theorem
gptkbp:bfsLayer 5