•Let All be a vocabulary
consisting of all relations on N
All = P(N) [ P(N2) [ P(N3) [ …
•In All we have names for <, +, /,
…
•
•Definition FO(All) = FO over vocabulary All
•Interpretation: consider
only ordered domains, assimilate with {0, 1,
2, …, n-1}. Each relation R on N is
interpreted as its restriction to {0, 1, …, n-1}.
•
•Note: we can express EVEN in
FO(All) [why ?]