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Preprint Number 2125
2125. James Hanson Bounded ultraimaginary independence and its total Morley sequences E-mail: Submission date: 10 January 2022 Abstract:
We investigate the following model-theoretic independence relation:
b ⊥^{bu}_A c
if and only if bdd^u(Ab) ∩ bdd^u(Ac)
= bdd^u(A), where bdd^u(X) is the class of all
ultraimaginaries bounded over X. 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 then follows as an immediate corollary. Mathematics Subject Classification: 03C45 Keywords and phrases: |

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