O-minimal expansions of the reals - UBC Library Open Collections

UBC Theses and Dissertations

Featured Collection

UBC Theses and Dissertations

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
Creator	Ingram, Patrick Malte Josef
Publisher	University of British Columbia
Date Issued	2002
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.
Extent	3568227 bytes
Genre	Thesis/Dissertation
Type	Text
File Format	application/pdf
Language	eng
Date Available	2009-10-07
Provider	Vancouver : University of British Columbia Library
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.
DOI	10.14288/1.0079363
URI	http://hdl.handle.net/2429/13735
Degree	Master of Science - MSc
Program	Mathematics
Affiliation	Science, Faculty of; Mathematics, Department of
Degree Grantor	University of British Columbia
Graduation Date	2002-11
Campus	UBCV
Scholarly Level	Graduate
Aggregated Source Repository	DSpace

Item Media

ubc_2002-0430.pdf -- 3.4MB

Item Citations and Data

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.