# nLab Robinson consistency theorem

Robinson’s Joint Consistency Theorem: If $T_1$ is a consistent $L_1$-theory, and $T_2$ is a consistent $L_2$-theory, then their union $T_1 \cup T_2$ is consistent if and only if their intersection $T_1 \cap T_2$ is complete when viewed as a $(L_1 \cap L_2)$-theory.

Proof: Apply the Craig interpolation theorem. QED.

This may be used to demonstrate the Beth definability theorem.

Created on July 13, 2017 at 12:18:19. See the history of this page for a list of all contributions to it.