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by vjoel 4624 days ago
Transitive closure and connected components are not expressible in first-order logic, but maybe you are thinking of Fagin's 0-1 law for finite relational models[1]:

For a given first-order sentence s, as n -> infinity, the fraction of models of cardinality n that satisfy s approaches either 0 or 1.

[1] http://researcher.watson.ibm.com/researcher/files/us-fagin/t...