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• W2949877199 abstract "We develop a notion of forking for Galois-types in the context of Abstract Elementary Classes (AECs). Under the hypotheses that an AEC $K$ is tame, type-short, and failure of an order-property, we consider {bf Definition.} Let $M_0 prec N$ be models from $K$ and $A$ be a set. We say that the Galois-type of $A$ over $M$ emph{does not fork over $M_0$} iff for all small $a in A$ and all small $N^- prec N$, we have that Galois-type of $a$ over $N^-$ is realized in $M_0$. Assuming property (E) (see Definition 3.3) we show that this non-forking is a well behaved notion of independence, in particular satisfies symmetry and uniqueness and has a corresponding U-rank. We find conditions for a universal local character, in particular derive superstability-like property from little more than categoricity in a big cardinal. Finally, we show that under large cardinal axioms the proofs are simpler and the non-forking is more powerful. In [BGKV] it is established that this notion of non-forking is the only independence relation possible." @default.
• W2949877199 created "2019-06-27" @default.
• W2949877199 creator A5027331051 @default.
• W2949877199 creator A5063970932 @default.
• W2949877199 date "2013-06-27" @default.
• W2949877199 modified "2023-09-27" @default.
• W2949877199 title "Forking in Short and Tame Abstract Elementary Classes" @default.
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