Strength (mathematical logic)

The relative strength of two systems of formal logic can be defined via model theory. Specifically, a logic ${\displaystyle \alpha }$ is said to be as strong as a logic ${\displaystyle \beta }$ if every elementary class in ${\displaystyle \beta }$ is an elementary class in ${\displaystyle \alpha }$.^[1]

See also

• Abstract logic
• Lindström's theorem

References

1. 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