The syllabus is somewhat approximate and subject to change.
29 January  Introductory Meeting, Chapter 1 
1 February  Chapter 2 
Problem Set #1 due 8 February  
3–12 February  Chapter 3; Section 4.1 It's still worth reading Turing's original paper "On Computable Numbers", Proceedings of the London Mathematical Society s242 (1937), pp. 23065 (Oxford Journals Archive). Section 9 of that paper contains a fascinating justification of his definition of computability in terms of a "conceptual analysis" of the intuitive notion. It's also worth looking at his paper "Computing Machinery and Intelligence", Mind 59 (1950), pp. 43360 (JSTOR). 
Problem Set #2 due 19 February  
15–19 February  Chapters 5–6 
22 February  No Class: Long Weekend 
24 February  Chapters 6 
Problem Set #3 due 

26 February–4 March  Chapter 7, Section 8.1 There is a handout, "Coding Turing Machine Computations", that contains the definitions of a lot of the functions we need to do that. 
Problem Set #4 due 11 March  
7–11 March  Chapters 9–10 A somewhat less formal presentation of Tarski's definition of truth can be found in the handout "Tarski's Theory of Truth", which I use in other classes. Note that this definition is given for the language of arithmetic, and only for the standard interpretation of that language. But it might nonetheless prove helpful. 
Problem Set #5 due 18 March  
14–18 March  Section 11.1; Chapter 13 There is a handout that summarizes some of the important definitions and lemmas in the proof of the Compactness Theorem. 
21 March 
No Class: Snow Day 
23 March  Chapter 13 There is a handout that summarizes some of the important definitions and lemmas in the proof of the Compactness Theorem. There is another handout that contains the proof of the Closure Lemma that was presented in class. 
Problem Set #6 due 6 April  
25 March  Chapter 14 You should have a look also at the handout on the simplified sequent calculus, which is the formal system we will actually discuss. 
28 March–1 April  No Class: Spring Break 
4–13 April  Chapters 1415 You should have a look also at the handout on the simplified sequent calculus, which is the formal system we will actually discuss. There is also a handout containing the revised definition of "theory", and related notions, that we'll use in class. 
Problem Set #7 due 20 April  
15–27 April  Chapter 16 There is a handout that lists the axioms of the various theories we will discuss and sumamrizes the important results we will prove. 
Problem Set #8 due 4 May  
29 April–4 May  Chapter 17 You can find a very informal exposition of one form of the diagonal lemma here. You may also find it helpful to read the only slightly more formal exposition in §10 of this document. 
Problem Set #9 due 11 May  
19 May, 2pm  Final Examination 