The diameter of a Lascar strong type
We prove that a type-definable Lascar strong type has finite diameter. We also answer some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups.
The models of a non-multidimensional -stable theory
The small index property for quadratic spaces.
The structure of superilat graphs
We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.
The uncountable spectra of countable theories.
Theorems on groups of finite Morley rank analogous to theorems on finite groups.
Théorie de la classification
Théorie des modèles et conjecture de Manin-Mumford
There are Infinitely Many Countable Models of Strictly Stable Theories With no Dense Forking Chains
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...
Thorn orthogonality and domination in unstable theories
We study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories.
Travaux publiés par les membres du groupe «théories stables»