{"DOI":"10.2178/jsl/1146620158","abstract":"AbstractWe prove a categoricity transfer theorem for tame abstract elementary classes.Suppose thatKis a \u03c7-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let\u03bb \u2265 Max{\u03c7, LS(K+}.If K is categorical in \u03bb and \u03bb+, then K is categorical in \u03bb++.Combining this theorem with some results from [37]. we derive a form of Shelah's Categoricity Conjecture for tame abstract elementary classes:Suppose K is \u03c7-tame abstract elementary class satisfying the amalgamation and joint embedding properties. Let\u03bc0\u2254 Hanf(K).Ifand K is categorical in somethen K is categorical in \u03bc for all\u03bc.","author":[{"family":"Grossberg"},{"family":"Vandieren"}],"id":"unknown","issue":"02","issued":{"date-parts":[[2006]]},"language":"en","page-first":"553","publisher":"Cambridge University Press (CUP)","title":"Shelah's categoricity conjecture from a successor for tame abstract elementary classes","type":"article-journal","volume":"71"}