From the Course Info. Sheet:

Weeks 11-12: Revision classes (also all live online).

- Lecture 1 Introduction; Section 1.1

- Lecture 2 1.2

- Lecture 3 1.3

- Lecture 4 1.3.2 Ordered Pairs, Relations, Functions

- Lecture 5 1.4 Transitive Sets

- Lecture 6 2.1 Number systems: Inductive sets, Principle of Math.'l Induction

- Lecture 7 2.3 The Recursion Theorem: statement and applications [N.B. Omit Section 2.2]

- Lecture 8 2.3 The Recursion Theorem: Proof [N.B. Omit Thm. 2.18, and Example 2.19: Lines 617-635]

- Lecture 9 3 Wellorderings and ordinals pp25-26.

- Lecture 10 3 p26 + 3.1 Ordinal Numbers: Classification Theorem for Ordinals

- Lecture 11 3.1 Representation Thm. for WO's; Classification Theorem for WO's; Sect 3.2

- Lecture 12 3.2 Properties of Ordinals, Burali-Forti Lemma, sums of orderings

- Lecture 13 3.2 Products of Orderings, suprema of sets of ordinals, Recursion Theorem on On

- Lecture 14 3.2 Proof of Recursion Theorem on On, Ordinal Arithmetic

- Lecture 15 3.2 Properties of Ordinal Arithmetic

- Lecture 16 3.2 Further properties of Ordinal Arithmetic [NB Omit Lemma 3.42, Ex. 3.18]

- Lecture 17 4.1 Cardinality: Equinumerosity

- Lecture 18 4.1 Cantor-Schröder-Bernstein Theorem

- Lecture 19 4.1 Countability, WP the Wellordering Principle

- Lecture 20 4.2, 4.3 Cardinal Numbers, cardinal arithmetic

- Lecture 21 4.3 Cardinal arithmetic, Hessenberg's Theorem

- Lecture 22 4.3 Cardinal Arithmetic, cardinal exponentiation

- Lecture 23 4.3 Cardinal Arithmetic, the Generalized Continuum Hypothesis

- Lecture 24 4.3 Cardinal Arithmetic, the Generalized Continuum Hypothesis [N.B. Omit Note on Dedekind Finite Sets p.53]

- Lecture 25 5.1 Axiom of Replacement

- Lecture 26 5.2 Axiom of Choice

- Lecture 27 5.2 Axiom of Choice and its equivalents

- Lecture 28 6 Axiom of Foundation and the V-hierarchy

- Lecture 29 6 Ranks

- Lecture 30 6 Epsilon Induction

- The live on-line slots during Weeks 11 and 12 will be Revision/Problems Classes. Thus Mondays at 9.00, Tuesdays at 9.00 and 15.00.
If there are sufficient queries either about Theory or Exercises/problems, I'll record a session to answer those queries for viewing
later in each of these Weeks 11 and (after the break) Week 12.

Please tell me how you would like this to run, and send in your queries.

(The system is automated so the deadline for the marker is strict.) NB The homework is not part of the course assessment (they are voluntary) but is nevertheless a necessary part of the learning process: it is there for you to practise, and you would be wise to at least attempt them each week to enhance your understanding. The Homework questions are embedded in the course text - there are no separate sheets for this. The solutions are published accordingly gradually (see 'Exercise Solutions' below).

- Week 1 Exs. 1.2, 1.4, 1.11.

- Week 2 Exs. 1.12, 1.15, 1.26. (i) (if you find the last one easy, try part (ii)).

- Week 3 Exs. 2.3, 2.6 (a) & (f), 2.12(i).

- Week 4 Exs. 3.4, 3.6, 3.7.

- Week 5 Exs. 3.9, 3.10 (Do just N x Z isom. Z x Z ?), 3.13(ii)

- Week 6 Exs. 3.23(i), 3.27, 4.11(i).

- Week 7 Exs. 4.15(ii), 4.17 part (iii),4.20.

- Week 8 Exs. 4.34 (i) & (iii), 4.37, 4.38,

- Week 9 Exs. 5.1, 5.3, 5.7

- Week 10 Exs. 6.1,(i) and (iii); 6.2, 6.6 (use the result from Ex 6.5 for this last one) Set Monday 7th Dec.

- Exercises Solutions Ch. 1
- Exercises Solutions Ch. 2
- Exercises Solutions Ch. 3
- Exercises Solutions Ch. 4
- Exercises Solutions Ch. 5 and Ch. 6

For past examination papers: see Blackboard ( --> Student Resources --> Examinations --> Past Examinations).

A single sample examination question and answer.