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It is proved definability in FO+IFP of a global linear ordering on vertices of strongly extensional (L E) finitely branching graphs. In the case of finite L E graphs this also holds for FO+LFP. This gives capturing results for PTIME computability on the latter class of graphs by FO+LFP and FO+IFP, and also on the corresponding anti-founded universe HFA of hereditarily finite sets by a language Δ...
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