The Formalities
Christopher
L. Miller
Associate Professor
Department of
Mathematics
The Ohio
State University
231 W. 18th Avenue
Columbus, OH 43210
e-mail: (my last name) at math dot ohio hyphen state 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.
"The
virtue of model theory is its ability to organize succinctly the sort
of tiresome algebraic details associated with elimination theory.''
(G. Sacks, 1972)
A must-read: J.S. Milne's Tips for Authors; click here and then look for the link near the bottom of the left panel.
(Please contact me for e- or offprints of papers that have already been published.)
07/14/09. Expansions
of o-minimal structures on the real field by
trajectories of linear vector fields.
07/01/09. Generic
expansions of ordered structures, with A.
Dolich and C. Steinhorn.
11/29/08. Expansions
of the real field by open sets: definability
versus interpretability, with H. Friedman, K. Kurdyka, and P.
Speissegger.
Version 07/30/09.
Structures having o-minimal open core, with
A. Dolich and C. Steinhorn, to appear in Trans. Amer. Math. Soc.
2/19/06. ... 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 12/15/06. 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).
LAOS
(Logicians at Ohio State)
MAMLS
(Mid-Atlantic Mathematical Logic Seminar)
ASL (Association for Symbolic Logic)
Deconstructing
Evaluations , by Paul Trout