Introduction to Mathematical Logic (S12)

Lectures (by Asger Tornquist): Monday 8.15-10am and Friday 10.15am-12pm in Auditorium 7 (HCØ).

Recitation (with Kristian Moi): Tuesday 1.15pm-4pm in 1-0-10 (DIKU).

We will use the book "A Mathematical Introduction to Logic", by Herbert Enderton (Academic Press, 2001). The lectures will follow the book roughly, but generally the perspective given in the lectures (as well as certain details) will be slightly different from that of the book.

You are strongly encouraged to take notes in class so that you can refer back to the material from the lectures in the future.

Syllabus and list of exam questions: pdf.

Oral exam meeting times: pdf.

Course credit homework assignment: Available here: pdf. Must be handed to Kristian Moi in section on May 29, 2012. Absolutely no extensions without a doctor's note!

Replacement lecture: There will be an extra lecture on June 12, 13.15-15.00 in Auditorium 7.

The lecture on Friday, June 8, 2012, will be given by Kristian Moi, since A.T. is in Texas.

Lectures, as it happened:

On June 1, 2012, I went through pp. 212-218. On Monday I will finish 3.3 and go through (most of) 3.4.

On May 29, 2012, I covered p. 206, as well as pp. 210-211.

On May 25, 2012, I went through pp. 204-206 (excluding the last theorem.) Notes from Sy Friedman's lecture.

On May 21, 2012, I covered pp. 155-156, pp. 182-187 (though not in great detail), pp. 202-204, and (partially) pp. 206-210 on Church's thesis. I will most likely not cover Ch. 3.1 and 3.2; read them at your own leisure (or not). Next time we will continue working our way through Ch. 3.3. A note containing the definition of recursive function that was given in class.

On May 14, 2012, I covered pp. 131-142, though I skipped the proof of the completeness theorem. Please read (at your leisure) pp. 142-145 on your own (starting with the Enumerability theorem.) On Monday, May 21, I will start on Ch. 3.

On May 11, 2012, I went through pp. 109-120 (except pp. 112-115 that were covered previously), by describing our deductive system, and proving the metatheorems of deduction (pp. 116-120.)

On May 7, 2012, I finished 2.2 by discussing definability in a structure (pp. 90-91) and homomorphisms (pp. 94-99). I skipped the "homomorphism theorem", which you can read on your own. I also went through pp. 112-115 about substitution and tautologies.

On April 27, 2012 I went through pp. 80-88. I also briefly mentioned the unique readability theorems of Section 2.3 (pp. 105-108). We will not return again to section 2.3: You are required to know the results (and what they mean to us), but you can skip the proofs if you like.

On April 23, 2012, I went through pp. 67-79 in the book.

Homework:

Homework for week 6: 3.3.4,5,6,8,9,10 (some of these refer to things introduced on pp. 219-220, which we will cover on Monday.)

Homework for week 5: 2.6.2, 3.3.1,2,3.

Homework for week 4: 2.5.1,2,3,6,8.

Homework for week 3: 2.2.11, 17(a), 18, 24, and 2.4.2, 3, 4, 5, and the exercises in the following document: pdf. You may also want to do 2.2.17(b) if you have extra time on your hands.

Homework for week 2: 2.2.1,3,4,6,16.

Homework for week 1: 2.1.1,3,5 and the exercises in the following document: pdf.

Nomenclashture: What I called a model in lecture is called a structure in the book. I will not change my usage, so I suggest that we use both words synonymously in this class. However, be warned that the word structure is used to mean something slightly different (though very related) in many other textbooks. On the other hand, there is almost universal agreement among textbooks (and mathematicians) as to what a model of a language means!