• Corpus ID: 245853802

Bounded ultraimaginary independence and its total Morley sequences

@inproceedings{Hanson2022BoundedUI,
  title={Bounded ultraimaginary independence and its total Morley sequences},
  author={James Hanson},
  year={2022}
}
We investigate the following model-theoretic independence relation: b | ⌣ bu A c if and only if bdd(Ab)∩bdd(Ac) = bdd(A), where bdd(X) is the class of all ultraimaginaries bounded overX. In particular, we sharpen a result of Wagner to show that b | ⌣ bu A c if and only if 〈Autf(M/Ab)∪Autf(M/Ac)〉 = Autf(M/A), and we establish full existence over hyperimaginary parameters (i.e., for any set of hyperimaginaries A and ultraimaginaries b and c, there is a b ≡A b such that b ′ | ⌣ bu A c). Extension… 

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