Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 57, Number 1 (2016), 59-71.
Improving a Bounding Result That Constructs Models of High Scott Rank
Let be a theory in a countable fragment of 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 that enumerates these extensions.
In this paper, we effectively construct a predecessor function for formulas defining types in this tree hierarchy as follows. Let with - and -theories on level and , respectively. Then if is a formula that defines a type for , our predecessor function provides a formula for defining its subtype in .
By constructing this predecessor function, we weaken an assumption for Sacks’s result.
Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 59-71.
Received: 17 October 2011
Accepted: 25 September 2013
First available in Project Euclid: 23 October 2015
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Goddard, Christina. Improving a Bounding Result That Constructs Models of High Scott Rank. Notre Dame J. Formal Logic 57 (2016), no. 1, 59--71. doi:10.1215/00294527-3328289. https://projecteuclid.org/euclid.ndjfl/1445606158