Models of high rank for weakly scattered theories
Author(s)Chan, Alice Shih Ying
Massachusetts Institute of Technology. Dept. of Mathematics.
Gerald E. Sacks.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (leaves 32-33).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology