Non-field-type completions do not interpret infinite fields
Let be a dense archimedean ordered abelian group, let be a strongly dependent and noiseless expansion, and let be a highly saturated elementary extension of . Let be the Shelah expansion and the completion structure. Non-field-type completion conjecture. If is not field-type, then does not interpret an infinite field. This is a conjectural strengthening of the modular decomposition: the field-type alternative is the only proposed source of an interpreted infinite field in the Shelah expansion.
References
Primary source
Erik Walsberg, “Externally definable quotients and NIP expansions of the real ordered additive group”, arXiv:1910.10572 (2020).
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