Show simple item record

dc.contributor.advisorLaskowski, Michael Cen_US
dc.contributor.authorShaw, Christopher Scotten_US
dc.date.accessioned2008-10-11T05:44:04Z
dc.date.available2008-10-11T05:44:04Z
dc.date.issued2008-07-28en_US
dc.identifier.urihttp://hdl.handle.net/1903/8545
dc.description.abstractThe 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.extent306560 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.titleWeakly o-minimal structures and Skolem functionsen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledModel theoryen_US
dc.subject.pquncontrolledweakly o-minimalen_US
dc.subject.pquncontrolledmathematical logicen_US
dc.subject.pquncontrolledskolem functionen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record