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Detailed view PhD thesis
University of California, Berkeley (20/12/2008), Thomas Scanlon (Dir.)
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Types in o-minimal theories
Janak Ramakrishnan1

We extend previous work on classifying o-minimal types, and develop several applications. Marker developed a dichotomy of o-minimal types into "cuts" and "noncuts," with a further dichotomy of cuts being either "uniquely" or "non-uniquely realizable." We use this classification to extend work by van den Dries and Miller on bounding growth rates of definable functions in Chapter 3, and work by Marker on constructing certain "small" extensions in Chapter 4. We further sub-classify "non-uniquely realizable cuts" into three categories in Chapter 2, and we give define the notion of a "decreasing" type in Chapter 5, which is a presentation of a type well-suited for our work. Using this definition, we achieve two results: in Chapter 5.2, we improve a characterization of definable types in o-minimal theories given by Marker and Steinhorn, and in Chapter 6 we answer a question of Speissegger's about extending a continuous function to the boundary of its domain. As well, in Chapter 5.3, we show how every elementary extension can be presented as decreasing.
1:  ICJ - Institut Camille Jordan
model theory – o-minimality

Types in o-minimal theories
We extend previous work on classifying o-minimal types, and develop several applications. Marker developed a dichotomy of o-minimal types into "cuts" and "noncuts," with a further dichotomy of cuts being either "uniquely" or "non-uniquely realizable." We use this classification to extend work by van den Dries and Miller on bounding growth rates of definable functions in Chapter 3, and work by Marker on constructing certain "small" extensions in Chapter 4. We further sub-classify "non-uniquely realizable cuts" into three categories in Chapter 2, and we give define the notion of a "decreasing" type in Chapter 5, which is a presentation of a type well-suited for our work. Using this definition, we achieve two results: in Chapter 5.2, we improve a characterization of definable types in o-minimal theories given by Marker and Steinhorn, and in Chapter 6 we answer a question of Speissegger's about extending a continuous function to the boundary of its domain. As well, in Chapter 5.3, we show how every elementary extension can be presented as decreasing.
model theory – o-minimality

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