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Does every sparse random graph model satisfying a zero-one law admit a computable Scott sentence that captures its almost-sure theory?

Related: Fagin's zero-one law for first-order logic on dense random graphs, Barany-Bollobas sparse zero-one law conjecture, Scott rank spectrum theorem for countable structures

The first paper studies limit laws for sparse random graphs, establishing which first-order properties hold with probability zero or one in certain random graph models. The second paper develops computable Scott analysis, which asks how descriptively simple a sentence can be while still uniquely identifying a structure up to isomorphism. The open problem is whether the almost-sure theory of a sparse random graph model that obeys a zero-one law can always be witnessed by a single computable Scott sentence, meaning a sentence of bounded quantifier complexity that pins down the almost-sure isomorphism type of the limit object in a computably explicit way.

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