Math 229: Model Theory
Spring 2015
General Information
Course Time and Place: TuTh 9:30-11am, 61 Evans
Instructor: Thomas Scanlon
e-mail address: scanlon@math.berkeley.edu
Office: 723 Evans
Office Hours: Wednesdays 12:30pm-2pm & Fridays 2:30pm-4pm
Announcements
Plan and Notes
This course will concentrate on the model theory of
valued fields following original sources. Lecture notes prepared by
students in the class will appear in due time.
- Our notes are transcribed and
edited by the students in the class. This document will be updated
routinely throughout the Spring 2015 semester.
- The theory of algebraically closed nontrivially valued fields. We
begin by recounting Abraham Robinson's theorem that the theory of algebraically
closed nontrivially closed valued fields is model complete, presented in
Section 3.4 of his book Complete Theories, North-Holland (1956) which
is available in the library at call number QA 9 R6. For algebraic
background, Robinson cites Wolfgang Krull,
Allgemeine Bewertungstheorie,
J. Reine Angew. Math. 167, 160-196 (1932). For a
textbook account of valuation theory, one might
consult Otto Endler, Valuation Theory, Springer (1972). Franz-Viktor Kuhlmann
has made available a draft
of his planned book on valuation thory with special emphasis on its
connections to model theory.
- For the week of March 17th and 19th, we will take a break from the
model theory of valued fields focusing instead on the Keisler-Shelah
isomorphism theorem. A detailed account is available in the book
by Chang and Keiler in the section on ultraproducts which are saturated.
- Class will not meet during the week of April 7th.
- For the theorem on quantifier elimination for the theory of
the p-adic numbers with analytic functions we will follow the
original proof of Denef and van den Dries closely. You can find
the details in “p-adic and real subanalytic sets”,
Annals of Mathematics (2) 128 (1988), no. 1, 79 - 138..
- A clear presentation of the Weierstrass preparation theorem
can be found in section II.2 of Géométrie Analytique Rigide
et Applications (QA247 F73) by Fresnel and van der Put.
We will have four make-up lectures during RRR week scheduled as follows:
- Monday, May 4th, 10am-12noon in 736 Evans
- Monday, May 4th, 2pm-4pm in 736 Evans
- Tuesday, May 5th, 10am-12noon in 736 Evans
- Tuesday, May 5th, 2pm-4pm in 891 Evans
Homework