Thickness, and a categoric view of type-space functors

Tom 179 / 2003

Itay Ben-Yaacov Fundamenta Mathematicae 179 (2003), 199-224 MSC: 03C95, 03C45. DOI: 10.4064/fm179-3-2


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.


  • Itay Ben-YaacovDepartment of Mathematics
    Massachusetts Institute of Technology
    77 Massachusetts Avenue, Room 2-101
    Cambridge, MA 02139-4307

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