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O-minimal expansions of the reals Ingram, Patrick Malte Josef
Abstract
We survey recent results on o-rninimal theories, and in particular o-minimal expansions of real closed fields. The recent work in the classification of reducts of the field of real numbers, largely the work of Peterzil, is presented, as is the basic groundwork of o-rriinimality. It is shown that if X ⊆ℝⁿ is semialgebraic, but not semilinear, then multiplication on ℝ may be defined locally in terms of X, modulo the vector space properties of the reals. If X \ K is not semilinear for any compact K, then the condition of locality can be removed.
Item Metadata
| Title |
O-minimal expansions of the reals
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2002
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| Description |
We survey recent results on o-rninimal theories, and in particular o-minimal expansions of real closed fields. The recent work in the classification of reducts of the field of real numbers, largely the work of Peterzil, is presented, as is the basic groundwork of o-rriinimality. It is shown that if X ⊆ℝⁿ is semialgebraic, but not semilinear, then multiplication on ℝ may be defined locally in terms of X, modulo the vector space properties of the reals. If X \ K is not semilinear for any compact K, then the condition of locality can be removed.
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| Extent |
3568227 bytes
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| Genre | |
| Type | |
| File Format |
application/pdf
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| Language |
eng
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| Date Available |
2009-10-07
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0079363
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2002-11
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.