Morley Rank in Homogeneous Models
Alexei Kolesnikov and G. V. N. G. Krishnamurthi
Source: Notre Dame J. Formal Logic Volume 47, Number 3
(2006), 319-329.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1163775439
Digital Object Identifier: doi:10.1305/ndjfl/1163775439
Mathematical Reviews number (MathSciNet): MR2264701
Zentralblatt MATH identifier: 1113.03030
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