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math.LO2006
Model theoretic stability and categoricity for complete metric spaces
Saharon Shelah, Alex Usvyatsov
We deal with the systematic development of stability for the context of approximate elementary submodels of a monster metric space, which is not far, but still very distinct from t…
math.LO2004
More on SOP_1 and SOP_2
Saharon Shelah, Alex Usvyatsov
This paper continues math.LO/0009087. We present a rank function for NSOP_1 theories and give an example of a theory which is NSOP_1 but not simple. We also investigate the connect…
math.LO2003
Banach spaces and groups - order properties and universal models
Saharon Shelah, Alex Usvyatsov
We deal with two natural examples of almost-elementary classes: the class of all Banach spaces (over R or C) and the class of all groups. We show both of these classes do not have…