Weakly o-minimal structures and Skolem functions
| dc.contributor.advisor | Laskowski, Michael C | en_US |
| dc.contributor.author | Shaw, Christopher Scott | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2008-10-11T05:44:04Z | |
| dc.date.available | 2008-10-11T05:44:04Z | |
| dc.date.issued | 2008-07-28 | en_US |
| dc.description.abstract | The monotonicity theorem is the first step in proving that o-minimal structures satisfy cellular decomposition, which gives a comprehensive picture of the definable subsets in an o-minimal structure. This leads to the fact that any o-minimal structure has an o-minimal theory. We first investigate the possible analogues for monotonicity in a weakly o-minimal structure, and find that having definable Skolem functions and uniform elimination of imaginaries is sufficient to guarantee that a weakly o-minimal theory satisfies one of these, the Finitary Monotonicity Property. In much of the work on weakly o-minimal structures, it is shown that nonvaluational weakly o-minimal structures are most "like" the o-minimal case. To that end, there is a monotonicity theorem and a strong cellular decomposition for nonvaluational weakly o-minimal expansions of a group. In contrast to these results, we show that nonvaluational weakly o-minimal expansions of an o-minimal group do not have definable Skolem functions. As a partial converse, we show that certain valuational expansions of an o-minimal group, called T-immune, do have definable Skolem functions, and we calculate them explicitly via quantifier elimination. | en_US |
| dc.format.extent | 306560 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/8545 | |
| dc.language.iso | en_US | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | Model theory | en_US |
| dc.subject.pquncontrolled | weakly o-minimal | en_US |
| dc.subject.pquncontrolled | mathematical logic | en_US |
| dc.subject.pquncontrolled | skolem function | en_US |
| dc.title | Weakly o-minimal structures and Skolem functions | en_US |
| dc.type | Dissertation | en_US |
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