# Definition of the union of structures?

Using the logic definition of a structure as a set coupled with finitary functions and relations, what is the definition of the union of two structures $\mathfrak{A}_1 \cup \mathfrak{A}_2$?

I encountered this in a discussion of preservation, where $\mathfrak{A}_1$ is an elementary substructure of $\mathfrak{A}_2$, if that makes any difference.

(I hate to ask such a basic question, but I can't find this anywhere)

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AFAIK $\mathfrak{A}_1 \cup \mathfrak{A}_2$ is defined only if $\mathfrak{A}_1, \mathfrak{A}_2$ have an upper bound, say $\mathfrak{A}$. Then the union is $\mathfrak{A}$ with functions and relations restricted to unions of corresponding sorts of $\mathfrak{A}_1, \mathfrak{A}_2$. – beroal Mar 29 '11 at 10:14

It makes sense that the models be related in some way as described in the above reference. For instance, if A is a model of $\phi$ and B is a model of $\neg\phi$, there can be no model which is the union of A and B.