5 found
Order:
  1.  35
    On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
    We study dp-minimal and strongly dependent theories and investigate connections between these notions and weight.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  2.  21
    More on SOP 1 and SOP 2.Saharon Shelah & Alexander Usvyatsov - 2008 - Annals of Pure and Applied Logic 155 (1):16-31.
    This paper continues the work in [S. Shelah, Towards classifying unstable theories, Annals of Pure and Applied Logic 80 229–255] and [M. Džamonja, S. Shelah, On left triangle, open*-maximality, Annals of Pure and Applied Logic 125 119–158]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering left triangle, open* among complete first order theories and the SOP2 property. We (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  3.  24
    On generically stable types in dependent theories.Alexander Usvyatsov - 2009 - Journal of Symbolic Logic 74 (1):216-250.
    We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent theories.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  4.  25
    Stable domination and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Annals of Pure and Applied Logic 162 (7):544-560.
    We develop the theory of domination by stable types and stable weight in an arbitrary theory.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  16
    Strict independence.Itay Kaplan & Alexander Usvyatsov - 2014 - Journal of Mathematical Logic 14 (2):1450008.
    We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley sequences which are (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark