Part 1 - University of Cambridge
Part 1 - University of Cambridge
Part 1 - University of Cambridge
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8<br />
First-Order Logic is too Weak<br />
For any first-order sentence ϕ, its class <strong>of</strong> finite models<br />
is trivially decidable (in LOGSPACE).<br />
Mod F (ϕ) = {A | A finite, and A |= ϕ}<br />
There are computationally easy classes that are not defined by any first-order<br />
sentence.<br />
• The class <strong>of</strong> sets with an even number <strong>of</strong> elements.<br />
• The class <strong>of</strong> graphs (V, E) that are connected.<br />
Anuj Dawar February 2013
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