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
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?