Models of high rank for weakly scattered theories

The Scott rank of a countable structure A, denoted sr(A), was observed by Nadel to be at most wA + 1, where wA4 is the least ordinal not recursive in A. Let T be weakly scattered and L(a,T) be E2-admissible. We give a sufficient condition, the B,-hypothesis, under which T has model A with w4A = a and sr(A) = a + 1. Given the B,-hypothesis, an iterated forcing argument is used to obtain a generic Ta D T such that Th has a model with the desired properties.

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

• Chan, Alice Shih Ying

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/1721.1/34557

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34557