116c: Mathematical Logic (Set Theory) – Syllabus

Math 116c. Tuesday, Thursday 2:30-4:00 pm. 151 Sloan. 

Instructor: Andres Caicedo, caicedo at caltech dot edu, 384 Sloan
Office Hours: By appointment

Grader: Todor Tsankov, todor at caltech dot edu, 260 Sloan
Office Hours: Monday 3-4pm

Math 116 provides an introduction to the basic concepts and results of mathematical logic and set theory. Math 116C will be devoted to set
theory. This is formalized following Cantor’s approach of considering ordinals and cardinals; we will present the Zermelo-Fraenkel axioms, explain how different mathematical theories can be modelled inside the set theoretic universe, and discuss the role of the axiom of choice. Once these basic settings have been studied, we will present different combinatorial results and describe Gödel’s constructible universe.

Grading Policy: The grade for this course will be based on homework assignments. There will be no exams.
Solutions to homework problems should be written individually, although collaboration is allowed unless otherwise stated. All references used to solve a problem should be explicitly mentioned, including those students you collaborated with. You cannot look up solutions from any source.
No late submissions of solutions are allowed, except for medical problems (note needed from the health center) or serious personal difficulties (note needed from the Deans office).

Please try to solve as many problems as it seems reasonable from each set.
Let me know if you find some problems to be too hard or too easy or to contain mistakes. Feedback is greatly appreciated.

Textbook: There is no required textbook. The following suggested references may be useful:

• Set theory for the working mathematician. By K. Ciesielski. Cambridge U. Press (1997), ISBN-10: 0521594650  ISBN-13: 978-0521594653
• Set theory. By A. Hajnal and P. Hamburger. Cambridge U. Press (1999), ISBN-10: 052159667X  ISBN-13: 978-0521596671
• Set theory. By T. Jech. Springer (2006), ISBN-10: 3540440852  ISBN-13: 978-3540440857
• Discovering modern set theory. By W. Just and M. Weese. Vol I. AMS (1995), ISBN-10: 0821802666 ISBN-13: 978-0821802663
  Vol II. AMS (1997), ISBN-10: 0821805282 ISBN-13: 978-0821805282
• Problems and theorems in classical set theory. By P. Komjath and V. Totik. Springer (2006), ISBN-10: 038730293X  ISBN-13: 978-0387302935
• Set theory. An introduction to independence proofs. By K. Kunen. North Holland (1983), ISBN-10: 0444868399  ISBN-13: 978-0444868398
• Notes on set theory. By Y. Moschovakis. Springer (2005), ISBN-10: 038728723X  ISBN-13: 978-0387287232

Additional references will be provided throughout the course.