Improving a bounding result that constructs models of high scott rank

Goddard, Christina (2016) Improving a bounding result that constructs models of high scott rank. Notre Dame Journal of Formal Logic, 57 1: 59-71. doi:10.1215/00294527-3328289


Author Goddard, Christina
Title Improving a bounding result that constructs models of high scott rank
Journal name Notre Dame Journal of Formal Logic   Check publisher's open access policy
ISSN 1939-0726
0029-4527
Publication date 2016-01-01
Sub-type Article (original research)
DOI 10.1215/00294527-3328289
Open Access Status Not Open Access
Volume 57
Issue 1
Start page 59
End page 71
Total pages 13
Place of publication Durham, NC, United States
Publisher Duke University Press
Language eng
Abstract Let T be a theory in a countable fragment of Lω1,ω whose extensions in countable fragments have only countably many types. Sacks proves a bounding theorem that generates models of high Scott rank. For this theorem, a tree hierarchy is developed for T that enumerates these extensions. In this paper, we effectively construct a predecessor function for formulas defining types in this tree hierarchy as follows. Let Tγ ⊂ T with T - and Tγ -theories on level and γ, respectively. Then if p (Tγ) is a formula that defines a type for Tγ , our predecessor function provides a formula for defining its subtype in T . By constructing this predecessor function, we weaken an assumption for Sackss result.
Keyword Bounds on Scott rank
Raw tree hierarchy
Weakly scattered theories
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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