Math 141a Mathematical logic I (Fall 2018)

Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Office hours: Th 2h30PM-4PM, SC 321H
Lectures: MF 12PM-1h15PM, SC 310

Course assistant: David Stoner
Email: dstoner (at) college
Office hours: Tuesday 4-5PM, SC 530

Canvas page (for administrivia, hw solutions)

Latest news / Announcements

• August 13, 2018: This webpage is online, hurray! Please read the syllabus.
• September 6, 2018: This week, I will hold office hours on Thursday 5-6PM in SC 321H.
• September 28, 2018: Please welcome our new course assistant, David Stoner!
• October 5, 2018: The take home midterm exam will be handed out on October 15, 2018 and due back two days later. More information.
• October 5, 2018: Office hours on Thursday, October 11 will be held by David from 2h30pm to 4pm in the math lounge.
• October 12, 2018: I will hold additional office hours today, 4-5PM in SC 321H.
• November 20, 2018: The take home last exam will be handed out on December 3, 2018 and due back two days later. More information.

Main course reference

• Bruno Poizat, A course in model theory - an introduction to contemporary mathematical logic, Springer-Verlag, 2000.

Exams

All the exams, including solutions, are now on Canvas.

Assignments

Will be posted here.

• Assignment 1 (due Friday, September 14). Latex source.
• Assignment 2 (due Friday, September 21). Latex source. Last updated on Monday, September 17 (in problem 3, gamma has to be at least 2).
• Assignment 3 (due Friday, September 28). Latex source. Last updated on Friday, September 28 (in problem 1(a), lambda should be infinite; also fixed a small mistake in the definition of a generic graph - this shouldn't impact your solution).
• Assignment 4 (due Friday, October 5). Latex source.
• Assignment 5 (due Friday, October 12). Latex source.
• Assignment 6 (due Monday, October 22). Latex source.
• Assignment 7 (due Friday, October 26). Latex source.
• Assignment 8 (due Friday, November 2). Latex source.
• Assignment 9 (due Friday, November 9). Latex source. Last updated on Nov. 6 (fixed some typos).
• Assignment 10 (due Friday, November 16). Latex source. Last updated on Nov. 15 (minor typo fixed).
• Assignment 11 (due Friday, November 30). Latex source. Note that you only have to do five of the problems.

Assignment solutions are posted regularly on Canvas.

Reading assignments

• For the week of Sep. 10-Sep. 14: Sections 8.1-8.3 in Poizat.

• For the week of Sep. 17-Sep. 21: Sections 8.2-8.3 and Chapter 1 in Poizat.

• For the week of Sep. 24-Sep. 28: Chapters 1 and 2.1, 2.2 in Poizat.

• For the week of Oct. 1-5: Chapters 2 and 3 in Poizat.

• For Friday, Oct. 12: Chapter 3 in Poizat.

• For the week of Oct. 15-19: Sections 4.1-4.2 in Poizat.

• For the week of Oct. 22-26: The notes on the completeness theorem.

• For the week of Oct. 29-Nov. 2: The notes on computability and arithmetic.

• For the week of Nov. 5-Nov. 9: The notes on Arrow's impossibility theorem.

• For the week of Nov. 12-Nov. 16: The notes on Compactness and graph coloring, and on Nonstandard analysis.

• For the rest of the semester: The notes on the model theory of fields.

Other course documents

• Notes on the Model theory of fields. (Updated Nov. 29, 2018)
• Notes on Nonstandard analysis. (Updated Nov. 13, 2018)
• Notes on Compactness and graph colorings.
• Notes on Arrow's impossibility theorem (last updated Nov. 5, 2018).
• Notes on Computability and arithmetic.
• Notes on the completeness theorem (last updated Nov. 1, 2018).
• Notes on Skolem's paradox.
• Notes on the infinite "prisonners and hats" puzzle.
• Course syllabus (last updated September 6, 2018) .
• Tentative schedule (last updated August 13, 2018, now outdated).

Other resources

• If you need a refresher on the very basics (proofs, relations, functions, injection, surjections, bijections, etc.), my Concepts of Mathematics lecture notes (taken from a class I taught in 2014 at Carnegie Mellon University) could be helpful.
• For logic generally:
  • Herbert B. Enderton, A mathematical introduction to logic, 2nd ed., Academic Press, 2001.
  • Kenneth Kunen, The foundations of mathematics, College publications, 2009.
• For set theory:
  • Karel Hrbacek and Thomas Jech, Introduction to set theory, 3rd ed., Marcel Dekker, 1999.
  • Kenneth Kunen, Set theory, revised ed., College publications, 2011.
• For model theory:
  • C.C. Chang and H. Jerome Keisler, Model theory, 3rd ed., Dover, 2012.
  • Gerald H. Sacks, Saturated model theory, 2nd ed., World Scientific, 2009.
• For nonstandard analysis:
  • Robert Goldblatt, Lectures on the Hyperreals. Springer-Verlag, 1998.
  • Mark McKinzie and Curtis Tuckey, Higher Trigonometry, Hyperreal Numbers, and Euler's Analysis of Infinities. Mathematics Magazine 74, no. 5 (Dec., 2001), pp. 339-368.
  • H. Jerome Keisler, Elementary Calculus: An Infinitesimal Approach, 3rd ed., Dover, 2012.
  • Karel Hrbacek, Olivier Lessmann, and Richard O'Donovan. Analysis with ultrasmall numbers. CRC Press, 2015.
• Other references:
  • A metareference: Teach yourself logic is a book listing references on logic.
  • Maryanthe Malliaris' survey article on some recent research in model theory, from a general mathematical point of view.
  • Douglas R. Hofstadter, Gödel, Escher, Bach: an eternal golden braid, Basic books, 1999. (a book about computability and logic for a general audience).