Detailed view  PhD thesis 
University of California, Berkeley (20/12/2008), Thomas Scanlon (Dir.) 
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Types in ominimal theories 
Janak Ramakrishnan^{1} 
We extend previous work on classifying ominimal types, and develop several applications. Marker developed a dichotomy of ominimal types into "cuts" and "noncuts," with a further dichotomy of cuts being either "uniquely" or "nonuniquely 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 subclassify "nonuniquely 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 wellsuited for our work. Using this definition, we achieve two results: in Chapter 5.2, we improve a characterization of definable types in ominimal 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 – ominimality 
Types in ominimal theories 
We extend previous work on classifying ominimal types, and develop several applications. Marker developed a dichotomy of ominimal types into "cuts" and "noncuts," with a further dichotomy of cuts being either "uniquely" or "nonuniquely 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 subclassify "nonuniquely 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 wellsuited for our work. Using this definition, we achieve two results: in Chapter 5.2, we improve a characterization of definable types in ominimal 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 – ominimality 
tel00338308, version 1  
http://tel.archivesouvertes.fr/tel00338308  
oai:tel.archivesouvertes.fr:tel00338308  
From: Janak Ramakrishnan  
Submitted on: Wednesday, 12 November 2008 16:24:31  
Updated on: Friday, 19 December 2008 15:49:55 