The Formalities
Christopher L. Miller
Professor
Department of
Mathematics
The Ohio State University
231 W. 18th Avenue
Columbus, OH 43210
e-mail: (my last name) at math dot osu dot edu
office: Math Tower 758
office phone: (614) 292-9363
FAX: (614) 292-1479
B.A. Mathematics, University of California, Santa Barbara,
1988.
Ph.D. Mathematics, University of Illinois at Urbana-Champaign,
1994. Thesis Advisor: L. van den Dries.
I am interested primarily in applications of
logic---specifically, model theory---to real analytic geometry,
geometric measure theory, asymptotic analysis, and questions of
differentiability and analyticity of real functions, via studying
sets and functions that are definable in "well-behaved'' (e.g.,
o-minimal) first-order structures on the field of real numbers.
Determining which structures should be regarded as well behaved is
part of the job.
(Please contact me for e- or offprints of papers that have already been published.)
07/18/11.
Basics of o-minimality and Hardy fields.
07/01/09.
Generic expansions of ordered structures, with A. Dolich
and C. Steinhorn.
4/10/11.
... for ``Avoiding the projective hierarchy in expansions of
the real field by sequences''.
2/5/05.
... for ``Geometric categories and o-minimal structures''.
9/2/03.
... for ``Expansions of the real field with power functions''.
These are miscellaneous observations and results that are not necessarily intended for publication, especially in their present form. Please regard them as such.
03/25/09. AP-sets of rationals define the natural numbers,
with A. Dolich.
Revised
04/25/11. A trichotomy for expansions of R_{an} by
trajectories of analytic planar vector fields (with Patrick
Speissegger).
Revised
12/15/06. A weak growth dichotomy for d-minimal expansions of
the real field.
Revised
12/15/06. Definable choice in d-minimal expansions of ordered
groups.
Revised
12/15/06. D-minimal expansions of the real field have the
exchange property.
8/7/03.
Status of the o-minimal two-group question (with Sergei
Starchenko).