# first order logic – Downward Lowenheim Skolem over an uncountable vocabulary

Downward Lowenheim Skolem says that there exists even a countable model for a set `F` of first order logic formulas, if

• the vocabulary and variables are countable
• `F` is satisfiable

Can one show a counterexample for the case where the assumption `countable vocabulary` is not fulfilled,
i.e. give an uncountable vocabulary together with a formula set `F` over this vocabulary, such that `F` is satisfiable but has no countable model?