David Marker

Professor Emeritus

LAS Distinguished Professor

Department of Mathematics, Statistics, and Computer Science

University of Illinois at Chicago

University of Illinois at Chicago

851 S. Morgan St. (M/C 249)

Chicago, IL 60607-7045

e-mail:marker@uic.edu

office phone: (312) 996-3069

FAX: (312) 996-1491

- I've retired as of May 2019.
- Previous Courses

- real algebraic geometry and real analytic geometry
- exponentiation
- differential algebra

- Logaritmic-exponential power series (with Lou van den Dries and Angus Macintrye)
- An introduction to the Model Theory of Fields
- Model theory of differential fields
- A survey article on Model theory and real exponentiation submitted to the AMS Notices.
- A failure of quantifier elimination (with A. Macintyre)
- Levelled o-minimal structures (with C. Miller)
- Differential Galois theory III: some inverse problems (with A. Pillay)
- A survey article Strongly minimal sets and geometry on the pregeometries of strongly minimal sets and Hrushovski's application to diophanitne geometry.
- Slides from 10/17 Berkeley logic colloquium on logarithmic-exponential series.
- Lecture notes from my seminar on ACFA are available here.
- Logarithmic-exponential series (with L. van den Dries and A. Macintyre)
- Manin kernels
- MSRI survey on Model theory of differential fields
- MSRI survey Introduction to Model Theory
- My book
*Model Theory: an Introduction*, an introductory text in model theory has just been published by Springer (Graduate Texts in Mathematics 217). Here are:- A detailed summary of contents
- An excerpt from the introduction
- A list of known errors

- Lecture notes on Descriptive Set Theory
- slides from lecture at RSME-ASM meeting in Seville (pdf file)
- slides from lecture at Notre Dame on Vaught's Conjecture for Differentially Closed Fields Part I , Part II (pdf files)
- Decidability of the Natural Numbers with the Almost-All Quantifier with Ted Slaman (pdf)
- Remarks on Zilbers Pseudoexponentiation (pdf)
- The Borel Complexity of Isomorphism for Theories with Many Types (pdf)
- Some Lecture Notes from Graduate Topics Course on Infinitary Logics and Abstract Elementary Classes
- Lecture Notes on Infintary Logic
- David Kueker's lecture Notes

- Slides from a lecture on Harrington's Proof that counterexamples to Vaught's Conjecture have arbitrarily large Scott rank below omega_2
- Slides from lecture on Model Theory and Differential Algebraic Geometry at 2012 AMS Meeting in Boston
- Uncountable real closed fields with PA integer parts (with Charles Steinhorn)
- LAS Distinguished Professor Lecture Notes and Photos March 19, 2013
- Degrees of Models of Arithmetic my 1983 Yale PhD thesis
- Classifying Pairs of Real Closed Fields Angus Macintyre's 1967 Stanford Thesis
- Turing degree spectra of differentially closed fields, joint with Russell Miller
- Decidability of the natural numbers with the almost-all quantifier joint with Ted Slaman (unpublished 2008 manuscript).
- Representing Scott sets in algebraic settings, joint with Alf Dolich, Julia Knight and Karen Lange
- Logical Complexity of Schanuel's Conjecture AMS Meeting in Charleston, March 2017.
- Fifty Years in the Model Theory of Differential Fields ASL Lecture at JMM Baltimore, January 2019.
- Lecture Notes on Model Theory of Valued Fields Fall 2018
- Model Theory and Machine Learning Model Theory and Mathematical Logic, U. Maryland , June 2019
- Model Theory of Differential Closures AMS Special Session lecture at JMM Denver, January 2020.

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