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2016 Improving a Bounding Result That Constructs Models of High Scott Rank
Christina Goddard
Notre Dame J. Formal Logic 57(1): 59-71 (2016). DOI: 10.1215/00294527-3328289


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 TγTδ with Tγ- and Tδ-theories on level γ and δ, respectively. Then if p(Tδ) is a formula that defines a type for Tδ, our predecessor function provides a formula for defining its subtype in Tγ.

By constructing this predecessor function, we weaken an assumption for Sacks’s result.


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Christina Goddard. "Improving a Bounding Result That Constructs Models of High Scott Rank." Notre Dame J. Formal Logic 57 (1) 59 - 71, 2016.


Received: 17 October 2011; Accepted: 25 September 2013; Published: 2016
First available in Project Euclid: 23 October 2015

zbMATH: 06550120
MathSciNet: MR3447725
Digital Object Identifier: 10.1215/00294527-3328289

Primary: 03C70, 03D60

Rights: Copyright © 2016 University of Notre Dame


Vol.57 • No. 1 • 2016
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