منابع مشابه
Forking 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 کاملForking in Short and Tame Aecs
We develop a notion of forking for Galois-types in the context of AECs. Under the hypotheses that an AEC K is tame, type-short, and failure of an order-property, we consider Definition 1. Let M0 ≺ N be models from K and A be a set. We say that the Gaois-type of A over M does not fork over M0, written A^ M0 N , iff for all small a ∈ A and all small N− ≺ N , we have that Gaois-type of a over N− i...
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 کاملShelah’s Eventual Categoricity Conjecture in Tame Aecs with Primes
A new case of Shelah’s eventual categoricity conjecture is established: Theorem 1. LetK be an AEC with amalgamation. WriteH2 := i2i(2LS(K))+ + . Assume that K is H2-tame and K≥H2 has primes over sets of the form M∪{a}. If K is categorical in some λ > H2, then K is categorical in all λ′ ≥ H2. The result had previously been established when the stronger locality assumptions of full tameness an...
متن کاملEquivalent Definitions of superstability in Tame Abstract Elementary Classes
ELEMENTARY CLASSES RAMI GROSSBERG AND SEBASTIEN VASEY Abstract. In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no lon...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2016
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2015.51