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• W2339569523 abstract "elementary classes Shelah suggested in [26] abstract elementary classes (AEC) as a platform to study model theoretic concepts in a more general setting. He studies a class K of structures in a fixed similarity type τ , but does not define any specific language. Instead he gives axioms for (K,4K) , where 4K is a relation between the models of the class. The class (K,4K) is for example assumed to be closed under isomorphisms, behave well with respect to 4K -increasing chains and have a downward LowenheimSkolem number LS(K) . If B is a subset of a structure A ∈ K , there is a 4K elementary substructure of A containing B of cardinality at most LS(K)+|B| . This context generalizes an elementary class (Mod(T ),4) , where 4 is the elementary substructure relation. In his Presentation Theorem Shelah showed that such a class can be presented as a class of reducts of models in an elementary class omitting a set of types. This" @default.
• W2339569523 created "2016-06-24" @default.
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• W2339569523 date "2006-12-19" @default.
• W2339569523 modified "2023-09-27" @default.
• W2339569523 title "FINITARY ABSTRACT ELEMENTARY CLASSES" @default.
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