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)

- 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.

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

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

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.

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.

- 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).

- 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.

- Herbert B. Enderton,
- 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.

- Karel Hrbacek and Thomas Jech,
- 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.

- C.C. Chang and H. Jerome Keisler,
- 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,
*GĂ¶del, Escher, Bach: an eternal golden braid*, Basic books, 1999. (a book about computability and logic for a general audience).