Bounds on Weak Scattering
Sacks, Gerald E.
Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, p. 5-31 / Harvested from Project Euclid
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The notion of a weakly scattered theory T is defined. T need not be scattered. For each $\cal A$ a model of T, let sr($\cal A$) be the Scott rank of $\cal A$. Assume sr($\cal A$) ≤ ω\sp A \sb 1 for all $\cal A$ a model of T. Let σ\sp T \sb 2 be the least Σ₂ admissible ordinal relative to T. If T admits effective k-splitting as defined in this paper, then $∃θ < σ\sp T \sb 2 such that sr($\cal A$) < θ for all $\cal A$ a model of T.
Publié le : 2007-01-14
Classification:  weakly scattered theories,  bounds on Scott rank,  03C70,  03D60 
@article{1172787542,
     author = {Sacks, Gerald E.},
     title = {Bounds on Weak Scattering},
     journal = {Notre Dame J. Formal Logic},
     volume = {48},
     number = {1},
     year = {2007},
     pages = { 5-31},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1172787542}
}

Sacks, Gerald E. Bounds on Weak Scattering. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp.  5-31. http://gdmltest.u-ga.fr/item/1172787542/