Part 1 - University of Cambridge
Part 1 - University of Cambridge
Part 1 - University of Cambridge
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15<br />
Stratifying Isomorphism<br />
In order to study the expressive power <strong>of</strong> first-order logic on finite structures, we<br />
considered one stratification <strong>of</strong> isomorphism:<br />
A ≡ q B<br />
if A and B cannot be distinguished by any sentence with quantifier rank at most q.<br />
An alternative stratification that is useful in studying fixed-point logics is based on<br />
the number <strong>of</strong> variables.<br />
A ≡ k B<br />
if A and B cannot be distinguished by any sentence with at most k distinct<br />
variables.<br />
Anuj Dawar February 2013
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