منابع مشابه
Interpreting groups and fields in simple, finitary AECs
We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable nitary abstract elementary classes: from a certain expression of `non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule out the presence of a non-classical grou...
متن کاملForking and superstability in Tame AECS
We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. T...
متن کاملGradings on simple algebras of finitary matrices
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
متن کاملCanonical forking in AECs
Boney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and local character. While doing this, we study more generally properties of independence relations for AECs and also prove a canonicity result for Shelah’s goo...
متن کاملCategoricity transfer in simple finitary abstract elementary classes
We continue to study nitary abstract elementary classes, de ned in [7]. We introduce a concept of weak κ -categoricity and an f-primary model in a א0 -stable simple nitary AEC with the extension property, and gain the following theorem: Let (K,4K) be a simple nitary AEC, weakly categorical in some uncountable κ . Then (K,4K) is weakly categorical in each λ ≥ min{κ,i(2א0 )+} . We have that if th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2007
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm195-3-3