CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC AND LOGIC-RELATED COURSES AND SEMINARS FOR FALL 2005 80-513 Seminar on Philosophy of Mathematics INSTRUCTORS: Jeremy Avigad (Carnegie Mellon) and Ken Manders (University of Pittsburgh) M 9:30-12:00 Room TBA (will alternative between CMU and Pitt) 12 units DESCRIPTION: One of the main reasons for the power of modern mathematics has been its use of algebraic structures in many different areas. The seminar aims to start to understand why this is powerful. 21-600 Mathematical Logic I Instructor: Peter Andrews MWF 11:30am-12:20pm Baker Hall A53 12 Units Description: The study of formal logical systems which model the reasoning of mathematics, scientific disciplines, and everyday discourse. Propositional calculus and first-order logic. Syntax, axiomatic treatment, derived rules of inference, proof techniques, computer-assisted formal proofs, normal forms, consistency, independence, semantics, soundness, completeness, the Lowenheim-Skolem Theorem, compactness. 21-603 Model Theory I Instructor: Rami Grossberg (rami@cmu.edu) MWF 1:30-2:20pm DH 1209 12 Units DESCRIPTION: Model theory is one of the four major branches of mathematical logic. There are many applications of model theory to algebra (e.g. field theory, algebraic geometry, number theory, and group theory), analysis (non-standard analysis, complex manifolds and the geometry of Banach spaces) and theoretical computer science (via finite model theory) as well as set theoretic topology and set theory. This course is the first in a sequence of three courses. The purpose of this course is to present the basic concepts and techniques of model theory with an emphasis on pure model theory. The main theorem of the course is Morley's theorem. It will be presented in a way that permits several powerful extensions. CONTENTS: Similarity types, structures. Downward Lowenheim-Skolem theorem. Construction of models from constants, applications of the compactness theorem, model completeness, elementary decideability results, Henkin's omitting types theorem, prime models. Elementary chains of models, some basic two-cardinal theorems, saturated models (characterization and existence), basic results on countable models including Ryll-Nardzewski's theorem. Indiscernible sequences, and connections with Ramsey theory, Ehrenfeucht- Mostowski models. Introduction to stability (including the equivalence of the order-property to instability), chain conditions in group theory corresponding to stability/superstablity/omega-stability, strongly minimal sets, various rank functions, primary models, and a proof of Morley's categoricity theorem. Basic facts about infinitary languages and abstract elementary classes, computation of Hanf-Morley numbers. PREREQUISITE: This is a graduate level course, while at the beginning the pace will be slow, the pace will speed up in the second half. In the past many of students where undergraduates, so the prerequisites are kept to the minimum of "an undergraduate-level course in logic. TEXT: Rami Grossberg, A course in model theory, a book in preparation. Most of the material (and more) appears in the following books: 1. C. C. Chang and H. J. Keisler, Model Theory, North-Holland 1990. 2. Bruno Poizat, A course in Model Theory, Springer-Verlag 2000. 3. S. Shelah, Classification Theory, North-Holland 1991. I will not use a text, but will provide access to my notes on a weekly basis. EVALUATION: Will be based on weekly homework assignments (20%), a 50 minutes midterm (20%) and a 3 hours in-class comprehensive final written examination (60%). COURSE WEBPAGE: www.math.cmu.edu/~rami/mt1.05.desc.html 21-804 Mathematical Logic Seminar Instructor: Ernest Schimmerling Thursdays, 12:00-1:20 Old Student Center 201 Description: The Mathematical Logic Seminar is scheduled to meet on Thursdays 12 - 1:20 during the coming semester. Please make an effort to keep this time slot free. Students, both undergraduate and graduate, are urged to enroll for 6 units in 21-804. Those invited to speak may enroll for a letter grade while others should audit. (I will sign Permission to Audit forms.) For additional information, please see http://www.math.cmu.edu/~eschimme/seminar.html 15-814 Type Systems for Programming Languages INSTRUCTOR: Robert Harper TuTh 1:30-2:50 p.m. WEH 5409 12 Units Web page: http://www.cs.cmu.edu/~rwh/courses/typesys