nLab
Robinson consistency theorem

Robinson’s Joint Consistency Theorem: If T 1T_1 is a consistent L 1L_1-theory, and T 2T_2 is a consistent L 2L_2-theory, then their union T 1T 2T_1 \cup T_2 is consistent if and only if their intersection T 1T 2T_1 \cap T_2 is complete when viewed as a (L 1L 2)(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.