Categoricity for transfinite extensions of modules

Abstract

For each deconstructible class of modules D, we prove that the categoricity of D in a big cardinal is equivalent to its categoricity in a tail of cardinals. We also prove Shelah's Categoricity Conjecture for (D, ), where (D, ) is any abstract elementary class of roots of Ext.

Keywords

• λ-categoricity
• categoricity in a tail of cardinals
• abstract elementary
• class, transfinite extensions of modules
• deconstructible class
• projective modules