Mathematical Logic Research - UC Berkeley Department of Mathematics

We have a large active group of researchers in several core areas of mathematical logic; including model theory, recursion theory and set theory. A number of members of the logic group belong to the Group in Logic and Methodology of Science, which runs a bi-weekly colloquium and has its own graduate students.

Faculty

Tenured and tenure-track:

John W. Addison (Emeritus), Theory of definability, descriptive set theory, model theory, recursive function theory.
Leo A. Harrington, Recursion theory, model theory, set theory.
Ralph N. McKenzie (Emeritus), General algebra, mathematical logic.
Thomas Scanlon, Model theory and applications to number theory.
Jack H. Silver, Mathematical logic, theory of sets.
Theordore A. Slaman, Recursion theory, mathematical logic.
Robert Solovay (Emeritus), Computer verification of formal proofs.
John R. Steel, Set theory, descriptive set theory, fine structure.
W. Hugh Woodin, Set theory, large cardinals, mathematical logic.

Visitors and postdoctoral fellows (2006-2007):

John Krueger, Set theory.
Jan Reimann, Theory of definability, Descriptive set theory, Model theory, Recursive function theory.

Courses

Undergraduate upper divison courses

Math 125. Mathematical logic.
Math 135. Set theory.

Graduate courses

Math 225A-225B. Metamathematics.
Math 227A-227B. Theory of recursive functions.
Math 229. Theory of models.
Math 235A-235B. Theory of sets.
Math 236. Metamathematics of set theory.

Topics courses and Seminars

2006-2007

Fall 2006

Math 290. Recursion Theory, Leo Harrington and Ted Slaman
Math 290. Model Theory, Tom Scanlon
Math 290. Model Theory: Metastability, Tom Scanlon
Math 290. Inner Model Theory, John Steel
Math 290. Set Theory, W. Hugh Woodin

Spring 2007

Current Thesis Students: Name (Adviser)

Meghan Anderson (Scanlon)
Uri Andrews (Scanlon)
Paul Baginski (Scanlon)
Adam Booth (LMS-student) (Steel)
Erik Closson (Steel)
Richard Dore (Woodin)
Kenneth Easwaran (LMS-student) (Scanlon)
Joseph Flenner (Scanlon)
Peter Gerdes (LMS-student) (Slaman)
Galen Huntington (LMS-student)
Benjamin Johnson (LMS-student) (Harrington)
Maryanthe Malliaris (LMS-student) (Scanlon)
Dominic McCarty (Woodin)
Koushik Pal (LMS-student) (Scanlon)
Janak Ramakrishnan (Scanlon)
Grigor Sargsyan (LMS-student) (Steel)
Farmer Schlutzenberg (Steel)
Lynn Scow (Scanlon)

Recent Ph.D.s: Name (Adviser) Thesis title

2007

Bernard Anderson (Slaman) Relative Properties of Reals
Johanna Franklin (Slaman) Aspects of Schnorr Randomness
John Goodrick (Scanlon) When Are Elementarily Bi-embeddable Models Isomorphic?
Alice Medvedev (Scanlon) Group-Like Minimal Sets in ACFA

2006

Xiannghui Shi (LMS student) (Woodin) Prewellorderings vs. Wellfounded Relations
First Position: Lecturer, Beijing Normal University

2005

Dragos Ghoica (Scanlon, Poonen) The Arithmetic of Drinfeld Modules
First Position:

2004

Clifton F. Ealy (Scanlon) Thorn Forking in Simple Theories
First Position: Cryptographer, NSA
Apollo Francis Hogan (Steel) General Topology Under the Axiom of Determinacy: the Beauty of Topology Without Choice
First Position:
Jason Horowitz (Slaman) Linearizing Countably Infinite Partial Orders
First Position:
Andreas Jue-Der Liu (Woodin) Self-Similarity at Singular Cardinals
First Position: Postdoctorial Fellowship, Hebrew University
Benjamin Miller (Steel) Full Groups, Classification, and Equivalence Relations
First Position:

2003

Andrés Caicedo (Steel, Woodin) Simply Definable Well-Orderings of the Reals
First Position: Posdoctoral fellow; Goedel Institute, Vienna Austria

2002

Bjorn Kjos-Hanssen (LMS-student) (Slaman) Lattice initial segments of the Turing degrees
First Position: Marie Curie Fellowship, Heidelberg University
Alf Onshuus (Scanlon) Thorn-forking in Rosy Theories
First Position: Lady Davis Fellow, Hebrew University

2001

John Clemens (Steel) Description Set Theory, Equivalence Relations, and Classification Problems in Analysis
First Position: Postdoc at Caltech
David Lippe (LMS-student) (Slaman) The Structure of the Delta-0-2 Turing Degrees
First Position: Renaissance Technologies
David Lippel (Harrington) Finitely axiomatizable omega-categorical theories
First Position:
Richard Zach (Silver) Hilbert's Program: Historical and Philosophical Perspectives
First Position: Assist, Prof. Univ. of Calgary

2000

Concetta Gomez (Harrington) Definability in p-adic Power Series Rings
First Position: Assistant Professor, Middlebury College
Aaron Zoble (Woodin) Stationary Reflection and the Determinacy of Inductive Games
First Position: (graduate school in economics)
Richard Ketchersid (Woodin) Toward AD_R from the Continuum Hypothesis and an omega_1 -dense ideal
First Position: Hedrick Post-doctoral Fellow, UCLA