Chris Miller

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 


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.

Research Interests

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.

Upgrades (or just corrections) for some published papers

pdf 01/27/21. Corrections to "Expansions of o-minimal structures by dense independent sets".

pdf 12/04/23. ... for "Expansions of the real field by canonical products".

pdf 05/30/23. Corrections to "Expansions of o-minimal structures by fast sequences".

dvipdfps 12/01/18. A correction to "Basics of o-minimality and Hardy fields".

dvi pdfps 01/19/17. ... for "Tameness in expansions of the real field".

dvi pdfps 9/7/12. ... for ''Avoiding the projective hierarchy in expansions of the real field by sequences''.

dvipdfps 11/14/12. ... for ''Geometric categories and o-minimal structures''.

dvipdfps 9/2/03. ... for ''Expansions of the real field with power functions''.

Unpublished notes

These are miscellaneous observations and results that are not necessarily intended for publication, especially in their present form. Please regard them as such.

pdf 05/28/23. A tameness condition on definably complete expansions of ordered fields.

pdf 02/07/23. Re-examination of an old question.

dvipdfps 03/25/09. AP-sets of rationals define the natural numbers, with A. Dolich.

dvipdfps Revised 04/25/11. A trichotomy for expansions of R_{an} by trajectories of analytic planar vector fields (with Patrick Speissegger).

dvipdfps Revised 12/15/06. A weak growth dichotomy for d-minimal expansions of the real field.

dvipdfps Revised 12/15/06. Definable choice in d-minimal expansions of ordered groups.

dvipdfps Revised 12/15/06. D-minimal expansions of the real field have the exchange property.

dvipdfps 8/7/03. Status of the o-minimal two-group question (with Sergei Starchenko).

Please contact me for e- or offprints of papers that have already been published.