The role of the omitting types theorem in infinitary logic.
The theorems of Beth and Craig in abstract model theory. II. Compact logics.
Thickness, and a categoric view of type-space functors
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...