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Bounds on Weak Scattering
Notre Dame Journal of Formal Logic 48 (1):5-31 (2007)
Abstract
The notion of a weakly scattered theory T is defined. T need not be scattered. For each a model of T, let sr() be the Scott rank of . Assume sr() ≤ ω\sp A \sb 1 for all 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 θσ\cal Aθ\cal A$ a model of TLinks
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Citations of this work
Classification from a computable viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
An introduction to the Scott complexity of countable structures and a survey of recent results.Matthew Harrison-Trainor - 2022 - Bulletin of Symbolic Logic 28 (1):71-103.
Computable structures in generic extensions.Julia Knight, Antonio Montalbán & Noah Schweber - 2016 - Journal of Symbolic Logic 81 (3):814-832.
Categories of Topological Spaces and Scattered Theories.R. W. Knight - 2007 - Notre Dame Journal of Formal Logic 48 (1):53-77.
Improving a Bounding Result That Constructs Models of High Scott Rank.Christina Goddard - 2016 - Notre Dame Journal of Formal Logic 57 (1):59-71.
References found in this work
Logic with denumerably long formulas and finite strings of quantifiers.Dana Scott - 1965 - Journal of Symbolic Logic 36 (1):1104--329.
Logic with Denumerably Long Formulas and Finite Strings of Quantifiers.Dana Scott, J. W. Addison, Leon Henkin & Alfred Tarski - 1971 - Journal of Symbolic Logic 36 (1):157-158.
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