An formula is one of the form , where is universal.
(a) Show that if an sentence in a language not containing function symbols (not even constant symbols) is true in , then it is true in some finite substructure of .
(b) Conclude that is not logically equivalent to any sentence.
(a) We have for some by assumption. We have to show that there are some finite substructure of such that
for the above .
How do I proceed from here?