Bounded ultraimaginary independence and its total Morley sequences
James Hanson

TL;DR
This paper explores a specific model-theoretic independence relation involving ultraimaginaries, establishing its properties, existence of Morley sequences, and connections to Shelah's concepts, with implications for theories with large cardinals.
Contribution
It introduces and analyzes bounded ultraimaginary independence, proving full existence, characterizing total Morley sequences, and linking to Shelah's notion of being 'based on' in simple unstable theories.
Findings
Characterization of ultraimaginary independence in terms of automorphism groups
Existence of total Morley sequences over hyperimaginary parameters
Connection between Morley sequences and Shelah's 'based on' concept
Abstract
We investigate the following model-theoretic independence relation: \def\indbu{{\rlap{\hspace11.9mu\vert}\lower7.5mu\smile}^{\!\mathrm{bu}}} b \indbu_A\hspace3mu c if and only if , where is the class of all ultraimaginaries bounded over . In particular, we sharpen a result of Wagner to show that b \indbu_A\hspace3mu c if and only if , and we establish full existence over hyperimaginary parameters (i.e., for any set of hyperimaginaries and ultraimaginaries and , there is a such that b' \indbu_A\hspace3mu c). Extension then follows as an immediate corollary. We also study total \hspace-5mu\indbu-Morley sequences (i.e., -indiscernible sequences satisfying…
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows
