Morley Rank in Homogeneous Models
Kolesnikov, Alexei ; Krishnamurthi, G. V. N. G.
Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, p. 319-329 / Harvested from Project Euclid
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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.
Publié le : 2006-07-14
Classification:  homogeneous models,  Morley rank,  03C45,  03C52,  03C05 
@article{1163775439,
     author = {Kolesnikov, Alexei and Krishnamurthi, G. V. N. G.},
     title = {Morley Rank in Homogeneous Models},
     journal = {Notre Dame J. Formal Logic},
     volume = {47},
     number = {1},
     year = {2006},
     pages = { 319-329},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163775439}
}

Kolesnikov, Alexei; Krishnamurthi, G. V. N. G. Morley Rank in Homogeneous Models. Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, pp.  319-329. http://gdmltest.u-ga.fr/item/1163775439/