Math 114L: Mathematical Logic

General Information

Time and Place: MWF 9-9:50am, Mathematical Sciences Building 5217 (notice the room change!)

Instructor: Matthias Aschenbrenner

E-mail address:

Mathematical Sciences Building 5614
Office Phone: (310) 206-8576
Office Hours: M 10-11:50pm, W 3-3:50pm, or by appointment. (I will not hold 'virtual' office hours.)

Discussion Section: Th 9-9:50am, Mathematical Sciences Building 5127 (!)
Teaching Assistant: Anush Tserunyan

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Click here to download the course handout.


The main objective of this course is to introduce you to mathematical logic through the study of two of its aspects:

1. Pure logic: Sentential logic and first-order logic, culminating in the proof of Gödel's Completeness Theorem (not to be confused with Gödel's Incompleteness Theorems).

2. Basic model theory: Applications of the Completeness Theorem, including the Löwenheim-Skolem Theorems, the Compactness Theorem; and a discussion of elementary equivalence.


The ability to formulate mathematical proofs. For this reason, you should have had some exposure to proof-writing before taking this course. Some knowledge of linear algebra or abstract algebra would also be useful, but is not strictly necessary. Please feel free to contact me if you'd like to take this course, but are unsure whether you have the right preparation.

Course Text

We will try to cover Chapters 1 and 2 of the book A Mathematical Introduction to Logic, Second Edition, by Herbert B. Enderton, Academic Press, 2001. The author of the textbook entertains a web page with errata and commentary.

Ideals, Varieties, and Algorithms


There will be a problem set assigned every week. The problems will range in difficulty from routine to more challenging. Completed solutions are to be handed in at the beginning of class on the due date specified on the respective homework set. No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade. You are encouraged to work together on the exercises, but any graded assignment should represent your own work.

Put the following information in the upper right hand corner of the first page:

   Your Name
   Math 114L, Homework # number.

On each additional page, put your name in the upper right-hand corner. Work single-sided, that is, write on only one side of each sheet of paper. STAPLE any homework that is more than one page long. Remove all perforation before submitting. Write legibly. Homework that fails to meet the above requirements will be marked "Unacceptable'' and returned unread.

Homework 1, due Friday, April 11. Solutions
Homework 2, due Friday, April 18. Solutions
Homework 3, due Friday, April 25. Solutions
Homework 4, due Friday, May 2. Solutions
Homework 5, due Friday, May 9. Solutions
Homework 6, due Friday, May 16. Solutions
Homework 7, due Friday, May 30. Solutions
Homework 8, due Friday, June 6. Solutions


There will be two Midterm examinations, on Monday, April 21 and Monday, May 19, in class. There will be a final exam on Tuesday, June 10, 11:30am-2:30pm, in MS  5217.

A review session for the Final Exam will be held on Monday, June 9, 12-2pm in MS 5203. (Notice the room change!)

Students with conflicts with the Midterm Exam in this course are responsible for discussing makeup examinations with me no later than two weeks prior to the exam.

No books, calculators, scratch paper or notes will be allowed during exams.

Grading policy: Homework: 20%. Midterm Exams: 20% each. Final Exam: 40%.

All scores and final grades will be available on the MyUCLA gradebook.

Historical Information

``Contrariwise,'' continued Tweedledee, ``if it was so, it might be; and if
it were so, it would be; but as it isn't, it ain't. That's logic.''
 Lewis Carroll  (1832-1898)

Click below to learn more about some of our logic heroes:

 Wilhelm Ackermann
 Paul Bernays
 George Boole
Georg Cantor
 Alonzo Church
 Paul Cohen
 René Descartes
 Richard Dedekind
 Adolf Fraenkel
 Gottlob Frege
 Gerhard Gentzen
 Kurt Gödel
 Jacques Herbrand
 David Hilbert
 Stephen Kleene
 Gottfried Wilhelm Leibniz
 Ramon Llull
 Leopold Löwenheim
 Augustus de Morgan
 John von Neumann
 Guiseppe Peano
 Emil Post
 Abraham Robinson
 Bertrand Russell
 Thoralf Skolem
 Alfred Tarski
 Alan Turing
 Alfred North Whitehead
 Ernst Zermelo

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