Suppose $K$ and $K'$ are two classes of structures in the same language which are both elementary classes. Is their union also an elementary class? Note, the classes do not have to be finitely axiomatizable, they just have to be axiomatizable.
2026-04-20 14:21:51.1776694911
Is the union of two elementary classes an elementary class?
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If $K$ and $K'$ are axiomatized by the sets $\Sigma$ and $\Sigma'$ of sentences, then $K\cup K'$ is axiomatized by $\{\alpha\lor\beta:\alpha\in\Sigma\text{ and }\beta\in\Sigma'\}$.