Geodesic
Thickness, and a categoric view of type-space functors
Itay Ben-Yaacov1
1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue, Room 2-101 Cambridge, MA 02139-4307 U.S.A.
Fundamenta Mathematicae, Tome 179 (2003) no. 3, pp. 199-224

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 between them and their classical counterparts. We conclude with several scattered results concerning cats and simplicity.
DOI : 10.4064/fm179-3-2
Keywords: define class thick cats compact abstract theories which contains particular semi hausdorff hausdorff first order cats prove class simplicity behaves first order theories consider well known first order notions interpretability stable dividing reduct propose analogous notions naturally expressed terms maps between type space functors prove several desirable properties notions connection between their classical counterparts conclude several scattered results concerning cats simplicity

Itay Ben-Yaacov 1

1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue, Room 2-101 Cambridge, MA 02139-4307 U.S.A. 
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Itay Ben-Yaacov. Thickness, and a categoric view of type-space functors. Fundamenta Mathematicae, Tome 179 (2003) no. 3, pp. 199-224. doi: 10.4064/fm179-3-2

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