In Skolem 1922 the author publishes a weak version of the Skolem-Löwenheim theorem which we call WLS and which according to [Wikipedia][1] says that every countable theory which is satisfiable in a model is also satisfiable in a countable model. My understanding is that WLS entails completeness in the sense of K. Gödel 1922. Does completeness entail WLS?

References:

K. Gödel 1929: *Über die Vollständigkeit des Logikkalküls*, Doctoral dissertation, University Of Vienna 

Skolem 1922: *Einige Bemerkungen zu axiomatischen Begründung der Mengenlehre*, 5th Scand. Math. Congress


  [1]: https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem