David Marker

Connecting

Teaching

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

Research Interests

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

An Invitation to Mathematical Logic

• Here is a link to the preface and table of contents
• Here is a link to a list of errors I am aware of. (last updated 5/27/25)

Some available preprints and Notes (postscript or pdf files)

• 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
  • An old list of known errors
  • A list of further errors compiled by Steffen Lempp
• 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
    • Sections 1 and 2
    • Section 3
    • Section 4
    • Section 5
  • David Kueker's lecture Notes
    • Lowenheim-Skolem Theorems and Countable Approximations
    • Finite Character
• 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 Jim Schmerl and Charlie 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.
• Scattered Sentences have Few Separable Randomizations with U. Andrews, I. Goldbring, S. Hachtman and H. J. Keisler
• Anti-classification results for groups acting freely on the line with F. Caldoroni, L. Motto Ros and A. Shani
• Lectures from BIRS workshop Model Theory of Differential Equations, Algebraic Geometry, and their Applications to Modeling
  • Lecture 1
  • Lecture 2
• Introductory Lectures from MSRI Program Decidability, definability and computability in number theory
  • Lecture 1
  • Lecture 2
  • Lecture 3
• Large stable fields Informal lectures, Spring 2021
• On the equations of Poizat and Lienard with J. Freitag, R. Jaoui and J. Nagloo
• Rigid differentially closed fields
• Some reflections on the work of Udi Hrushovski lecture Fields Workshop: From Geometric Stability Theory to Tame Geometry
• Strong minimal sets in differentially closed fields: Equations of Poizat and Lienard type Seminar IPM Tehran
• A Midwest Model Theory Meeting at UIC October 14-16, 2022 in honor of Charles Steinhorn's 70th birthday
• Fall 2023 Coven Wood Lectures at Wesleyan University
  • Poster
  • Lecture 1: Definability in Mathematics
  • Lecture 2: Model Theory and Differential Algebra
• Rigid Real Closed Fields with Charles Steinhorn