Source: Notre Dame J. Formal Logic
Volume 42, Number 3
We introduce the notion T does not omit obstructions. If a stable theory
does not admit obstructions then it does not have the finite cover property
(nfcp). For any theory T, form a new theory by adding a new unary
function symbol and axioms asserting it is an automorphism. The main result of
the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if has a model companion. The proof involves some
interesting new consequences of the nfcp.
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