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)
The closest thing I could find was at the bottom of page 144 of the following:
http://www.mathunion.org/ICM/ICM1970.1/Main/icm1970.1.0141.0150.ocr.pdf
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.