21-624 Topics in analysis: descriptive set theory
Instructor: Ernest Schimmerling
MWF 12:30
Room: Gates-Hillman 4101
12 units
Descriptive set theory combines analysis and logic.  The required
background is undergraduate level analysis, logic and set theory.  The
recommended textbook is Kechris, "Classical Descriptive Set Theory",
Graduate Texts in Mathematics 156, Springer-Verlag.  Another useful book
is Moschovakis, "Descriptive Set Theory".
         The topics to be covered include: Polish spaces (Baire space,
Cantor space, etc.); classical definability hierarchies (Borel
Hierarchy, Projective Hierarchy); effective definability hierarchies;
the Wadge hierarchy; complete sets, universal sets; separation;
reduction; uniformization; prewellordering; scales; perfect sets; Baire
measurability; Lebesgue measurability; Suslin operation; substitution
property; basis theorems; tree representations; proofs of determinacy
(Borel determinacy); applications of determinacy; definable winning
strategies; theorems on the boundedness of norms; theorems on the ranks
of wellfounded relations (Kunen-Martin); admissible ordinals; stable
ordinals.
     In addition to more standard graduate course mechanics, student 
enrolled for a grade will be assigned more advanced individual reading 
projects on which they will lecture towards the end of the semester.

21-700 Math Logic II
Instructor: Jose Iovino
MWF 11:30
Room: Wean Hall 7201
12 Units
In the first part of the course we will focus on the limitations of
first-order logic: Godel's Incompleteness Theorems, the undecidability
of first-order logic, and Tarski's theorem on the undefinablity of
truth. In the second part we will study extensions of first-order
logic (infinitary logics, second order logic, generalized
quantifiers), and we will prove Lindstrom's Theorems on the maximality
of first-order logic.
Textbooks:
M. Goldstern and H. Judah, "The Incompleteness Phenomenon", A K
Peters/CRC Press (July 30, 1998)
H.-D. Ebbinghaus, G. Flum, and W. Thomas, "Mathematical Logic",
Springer-Verlag, 1994.

21-803 Model Theory III
Rami Grossberg (Rami@cmu.edu)
URL: www.math.cmu.edu/~rami
MWF 3:30-2:20PM
Room: Wean Hall 7201
12 Units
This will be different than courses I offered in recent years. It will 
not depend on Model theory II.
This time I will concentrate in classification theory for first-order 
theories.
Prerequisites: Elementary model theory (half of 21-603) or permission of 
the instructor.
Text: There is no official text.
Some of the material appears in the following books:
J. Baldwin, Fundamentals of stability theory,
S. Buechler, Essential Stability theory.
A. Pillay, Stability
Bruno Poizat, A course in Model Theory, Springer-Verlag 2000.
Saharon Shelah, Classification Theory North-Holland 1991. This is the 
most important and the least readable book in model theory.

21-805 Lambda Calculus
Instructor: Rick Statman
with possible guest lecturers Henk Barendregt and Dana Scott
MWF 1:30
Room: Doherty Hall 1211
12 Units
Textbook: The Lambda Calculus by Henk Barendregt, North Holland 1981, 
ISBN 0 444 85490 8 (2nd edition & paperback editions OK)
Description:
@ Although an introductory graduate course the only
  prerequisite for this course is an undergraduate course
  in logic and computability theory.
@ Topics covered include
   (1)Basic properties of reduction and conversion
   (2)Reduction and conversion strategies
   (3)Calculability and representation of data types
   (4)Theory of Ershov numberings
   (5)Bohm's theorem, easy terms, and other exotic combinations
   (6)Solvability of functional equations (unification)
   (7)Combinators and bases
   (8)Simple and algebraic types
   (9)Labelled reduction and intersection types
   (10)Extensionality and the omega rule
@ Each of these topics includes several beautiful
   research problems. These range in difficulty from ones suitable
   for senior thesese to ones suitable for PhD dissertations.
   Students are free to pursue whichever problems appeal to them.
Requirements: Enrolled students can work together in teams to
produce lecture notes due at the end of the semester.