Schedule

This will be updated frequently during the semester.

Week	#	Day	Date	Content	Readings
				Background
1	1	Wed	Jan 5	Proof Types: Proof by cases, by contradiction, conditional. Contraposition.
	2	Fri	Jan 7	Definition by recursion. Mathematical induction.
2	3	Wed	Jan 12	Sets: Relations and functions.	(Ch.0-1)
	4	Fri	Jan 14	Denumerable and non-denumerable sets. Diagonalization.	(Ch.2-3)
				Propositional Logic
3	5	Wed	Jan 19	Formulas. Induction on the degree of formulas (Prob. 1.9). Semantics.	Ch.7, §1-5
	6	Fri	Jan 21	Axiomatic calculus. Soundness. Cut Rule. Deduction Theorem.	Ch.7, §6-7
4	7	Wed	Jan 26	Structural rules: IE, reductio, PIP	Ch.7, §8
	8	Fri	Jan 28	Weak completeness. Hintikka sets.	Ch.7, §9-10
5	9	Wed	Feb 2	Maximal consistent sets. Strong completeness	Ch.7, §11-13
				First-Order Logic
	10	Fri	Feb 4	Basic syntax. Mathematical structures. Basic semantics.	Ch.8, §1-4
6	11	Wed	Feb 9	BSD. Free and bound variables. Substitution in terms (Early course evals)	Ch.8, §4-6
	12	Fri	Feb 11	Substitution in formulas. First-order predicate calculus. Rules of instantiation	Ch.8, §9-10
7	13	Wed	Feb 16	Rules of generalization. Hintikka sets. Equivalence classes	Ch.8, §7 and 10
	14	Fri	Feb 18	Review session (Q&A).
		Wed	Feb 23	Study week
		Fri	Feb 25	Study week
8	15	Wed	Mar 2	Consistency. Maximal consistency. Henkin sets	Ch.8, §11-12
	16	Fri	Mar 4	Completeness	Ch.8, §13
				Limitative Results
9	17	Wed	Mar 9	Elementary arithmetic. Theories. Isomorphisms	Ch.10, §1-3
	18	Fri	Mar 11	Skolem's Theorem. Representability. Arithmeticity	Ch.10, §3-5
10	19	Wed	Mar 16	Coding. Diagonal function	Ch.10, §6
	20	Fri	Mar 18	Tarski's Theorem. Axiomatizability	Ch.10, §7-8
11	21	Wed	Mar 23	Subtheories of arithmetic: Baby, junior, and finitely axiomatized	Ch.10, §9-11
	22	Fri	Mar 25	First-order Dedekind-Peano Arithmetic.	Ch.10, §12-13
12	23	Wed	Mar 30	Undecidability. Church's Theorem	Ch.10, §13
	24	Fri	Apr 1	Gödel's First Incompleteness Theorem	Ch.10, §14
13	25	Wed	Apr 6	Gödel's Second Incompleteness Theorem	Ch.10, §15
	26	Fri	Apr 8	(No class; review session, EDUC 338)
				Final Exam
	E	Tue	Apr 12	Final exam: 9-12am, EDUC 211