Abstract
We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.
Citation
Alexei Kolesnikov. G. V. N. G. Krishnamurthi. "Morley Rank in Homogeneous Models." Notre Dame J. Formal Logic 47 (3) 319 - 329, 2006. https://doi.org/10.1305/ndjfl/1163775439
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