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Thickness, and a categoric view of type-space functors

Itay Ben-Yaacov (2003)

Fundamenta Mathematicae

We define the class of thick cats (compact abstract theories, which contains in particular semi-Hausdorff, Hausdorff and first order cats), and prove that in this class simplicity behaves as in first order theories. We consider well-known first order notions, such as interpretability or stable dividing/reduct, and propose analogous notions that can be naturally expressed in terms of maps between type-space functors. We prove several desirable properties of the new notions and show the connection...

Weak generic types and coverings of groups I

Ludomir Newelski, Marcin Petrykowski (2006)

Fundamenta Mathematicae

We introduce the notion of a weak generic type in a group. We improve our earlier results on countable coverings of groups and types.

When a first order T has limit models

Saharon Shelah (2012)

Colloquium Mathematicae

We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.

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