Math 770: Foundations of Mathematics
(Instructor: Steffen Lempp)
This is an introductory graduate course in mathematical logic. We will discuss
each of the four main subjects of logic: set theory, model theory, proof
theory, and computability theory. The main topics will include the axioms
of Zermelo-Fraenkel set theory with choice, ordinal and cardinal arithmetic,
the syntax and semantics of first-order logic, a first-order proof calculus,
the Completeness and Compactness Theorems, the Löwenheim-Skolem Theorems,
and the Gödel Incompleteness Theorems.
TEXTBOOK:
- Kenneth Kunen: The Foundations of Mathematics (College Publications)
REFERENCE BOOKS:
- Ebbinghaus, Flum, Thomas: Mathematical Logic (Springer-Verlag)
- Hinman: Fundamentals of Mathematical Logic (A. K. Peters/CRC Press)
- Shoenfield: Mathematical Logic (Routledge)
- Enderton: A Mathematical Introduction to Logic (Academic Press,
see class handouts on Presburger
arithmetic)
LECTURES:
Lectures will be given live at the regular time on Blackboard Collaborate
Ultra, accessible from Canvas and posted there for later viewing.
HOMEWORK:
Homework will be assigned intermittently throughout the semester and due at
noon on the dte given below.
- HW # 1 DUE 9/18: Chapter I: 2.1, 6.13, 6.17, 7.16, 7.23
(in an online version of the book, these are 2.1, 6.12, 6.16, 7.16, 7.24)
- HW # 2 DUE 10/9: Chapter I: 8.10, 8.13, 9.6, 11.15,
11.33, 12.14, 12.15, 12.18
(in an online version of the book, these are 8.10, 8.13, 9.6, 11.13,
11.33, missing, 12.14, and missing)
- HW # 3 DUE 10/16: Chapter I: 13.20, 14.14, 14.24
(in an online version of the book, these are 13.20, 14.12, and missing)
- HW # 4 DUE 10/26: Chapter II: 4.7, 7.18, 7.19, 8.5, 8.20,
8.25
- HW # 5 DUE 11/11: Chapter II: 10.6, 11.10, 11.11, 11.13,
12.23
- HW # 6 DUE 11/30: Chapter VI: 3.4, 3.28, 3.29, 3.30
TAKE-HOME FINAL EXAM:
Available on line here, due Friday, December 18,
at noon.
Prepared by
Steffen Lempp
(@math.wisc.edu">lemppmath.wisc.edu)