##  [Löwenheim–Skolem Property](/lowenheim-skolem-property) 

  ##  [Löwenheim–Skolem Property](https://mathlogic.quantumdictionary.io/lowenheim-skolem-property-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A family of results and the associated property for a logic or theory that constrain the cardinalities of models: typically the downward Löwenheim–Skolem theorem says a satisfiable set of sentences has a model of at most a certain smaller cardinality (often countable), while upward versions assert existence of larger models; together they express that satisfiability does not fix model cardinality