Strength (mathematical logic)

The relative strength of two systems of formal logic can be defined via model theory. Specifically, a logic $\backslash alpha$ is said to be as strong as a logic $\backslash beta$ if every elementary class in $\backslash beta$ is an elementary class in $\backslash alpha$.Heinz-Dieter Ebbinghaus Extended logics: the general framework in K. J. Barwise and S. Feferman, editors, Model-theoretic logics, 1985 {{isbn|0-387-90936-2}} page 43