Strength (mathematical logic)
Encyclopedia
The relative strength of two systems of formal logic
can be defined via model theory
. Specifically, a logic
is said to be as strong as a logic 
if every elementary class
in
is an elementary class in 
.
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
can be defined via model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
. Specifically, a logic
is said to be as strong as a logic if every elementary classElementary class
In the branch of mathematical logic called model theory, an elementary class is a class consisting of all structures satisfying a fixed first-order theory.- Definition :...
in
is an elementary class in .