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- W3140484208 abstract "We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs $$G(n,n^{-alpha })$$ given by Laskowski (Isr J Math 161:157–186, 2007) extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative but arbitrarily small in context. We give a necessary and sufficient condition for the theory of a Baldwin–Shi hypergraph to have atomic models. We further show that for certain well behaved classes of theories of Baldwin–Shi hypergraphs, the existentially closed models and the atomic models correspond." @default.
- W3140484208 created "2021-04-13" @default.
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- W3140484208 date "2021-04-05" @default.
- W3140484208 modified "2023-09-24" @default.
- W3140484208 title "The theories of Baldwin–Shi hypergraphs and their atomic models" @default.
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- W3140484208 doi "https://doi.org/10.1007/s00153-021-00765-8" @default.
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