Improving a bounding result for weakly-scattered theories

In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weakly-scattered theory. Using this predecessor function, we improve a recent bounding result by Sacks for weakly-scattered theories by removing the assumption of a predecessor function from the k-splitting hypothesis. We begin by giving an introduction to the infinitary logic [...] and admissible sets. We then outline results by Sacks that are important in the construction of the predecessor function. We introduce scattered and weakly-scattered theories and their related hierarchies, and explain how they relate to the well-known Scott hierarchy. Using the raw tree hierarchy, we present Sacks' constructive result called the Effective Recovery Process. Using all of these tools, we provide a proof of the existence of a predecessor function for the type definitions and then use it to improve the bounding result by Sacks.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Goddard, Christina M. (Christina Margaret)

Advisor dc:contributor.advisor

• Gerald E. Sacks.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34547

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34547