# Löwenheim–Skolem theorem

> theorem that, for any signature 𝜎, any infinite 𝜎-structure 𝑀 and any infinite cardinal 𝜅≥|𝜎|, there is a 𝜎‐structure 𝑁 of cardinality 𝜅 that is either an elementary substructure or an elementary extension of 𝑀

**Wikidata**: [Q1068283](https://www.wikidata.org/wiki/Q1068283)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Löwenheim–Skolem_theorem)  
**Source**: https://4ort.xyz/entity/l-wenheim-skolem-theorem


## References

1. Freebase Data Dumps. 2013