Hi,

This time I've problem with following exercise:

Let be a first-order language and for each let be a class of -structures.

Show that .

Here are some basic definitions from the book "Model Theory", W. Hodges (which could help):

Asentenceis a formula with no free variables. Atheoryis a set of sentences.

We say that is amodelof , or that istruein , when holds. Given a theory in , we say that is amodelof , in symbols , if is a model of every sentence in .

Let be a language and a class of -structures. We define the -theoryof , , to be the set (or class) of all sentences of such that for every structure in . We omit the subscript when isfirst-order: the theory of , , is the set of allfirst-ordersentences which are true in every structure in .

Thanks for any help.