# Elements of set theory, spring 2014

### Lecturer

### Scope

10 sp.

### Type

Intermediate studies

### Prerequisites

No special prerequisites.

### Description

Set theory is widely accepted as the foundation of mathematics. In this course, we will go through chapter 1-7 of Enderton's book Elements of Set Theory. The following topics will be covered: axioms and operations on sets, relations and functions, natural numbers, construction of real numbers, cardinal numbers, axiom of choice, orderings and ordinal numbers.

### Lectures

Weeks 3-8 and 11-18, Tuesday 12-14 in room B322 and Thursday 14-16 in room DK117.

Easter Holiday 17.-23.4.

contents | handout | last modified | |
---|---|---|---|

week 3 (Jan 14, 16) | chapter 1-2: introduction, axioms and operations | Jan 16, 22:30 | |

week 4 (Jan 21, 23) | chapter 3: ordered pairs, relations and orderings, equivalence relations. chapter 7: partial orderings | Jan 24, 20:50 | |

week 5 (Jan 28, 30) | chapter 3: equivalence relations, functions, axiom of choice | Jan 31, 13:40 | |

week 6 (Feb 4, 6) | chapter 4: construction of natural numbers, transitive sets, ordering on ω, recursion theorem | Feb 6, 23:30 | |

week 7 (Feb 11, 13) | chapter 4: arithmetic. chapter 5: integers | Feb 13, 23:30 | |

week 8 (Feb 18, 20) | chapter 5: rational numbers, Dedekind cuts | Feb 20, 23:50 | |

week 11 (Mar 11, 13) | chapter 5: real numbers | Mar 13, 17:00 | |

week 12 (Mar 18, 20) | chapter 6: equinumerosity, finite sets, cardinal arithmetic | Mar 20, 16:40 | |

week 13 (Mar 25, 27) | chapter 6: cardinal arithmetic, ordering cardinal numbers | Mar 27, 17:00 | |

week 14 (Apr 1, 3) | chapter 6: ordering cardinal numbers, axiom of choice, countable sets, absorption law of cardinals | Apr 3, 21:40 | |

week 15 (Apr 8, 10) | chapter 7: well orderings, isomorphisms, ordinal numbers | Apr 10, 17:00 | |

week 16 (Apr 15) week 17 (Apr 24) | chapter 7: ordinal numbers, transfinite induction and recursion, debts paid | Apr 24, 17:20 | |

week 18 (Apr 29) | chapter 7: debts paid, rank | Apr 29, 14:20 |

### Exams

There will be a midterm exam and a final exam.

Date | Time | Place | |
---|---|---|---|

Midterm Exam | Feb 28 | 10-12 | B120 |

Final Exam | May 9 | 10-12 | B321 |

Bibliography

Textbook: | H. Enderton, Elements of Set Theory, Academic Press. (Errata) |

References: | Introduction to Set Theory, Karel Hrbacek and Thomas Jech, 3rd Edition, Marcel Dekker. |

Set Theory for the Working Mathematician, Krzysztof Ciesielski, Cambridge University Press. |

### Exercise class

Group | Day | Time | Place | Teacher |
---|---|---|---|---|

1. | Friday | 10-12 | B321 | Miguel Moreno |

### Exercises

Date of exercise class | |
---|---|

1. | Jan 24 |

2. | Jan 31 |

3. | Feb 7 |

4. | Feb 14 |

5. | Feb 21 |

6. | Mar 14 |

7. | Mar 21 |

8. | Mar 28 |

9. | Apr 4 |

10. | Apr 11 |

11. | Apr 25 |

12. | May 2 |

13. | No exercise class |

### Grading

To pass the course, you need to take two course exams (midterm and final). Attending only one exam (even if you score full marks) is not sufficient. From each of the two exams, you can score (4 questions × 6 points =) 24 points. The passing mark for the course is around 24 points (the exact passing mark will be decided by the lecturer at the end of the semester according to the overall performances of the students).

By solving a certain amount of the exercise problems, you will be awarded extra points (see the table below for details). "Solving" here means that you have honestly tried to give solutions to the problems.

percentage of exercise problems solved | extra points |
---|---|

≥40% | 1 |

≥50% | 2 |

≥60% | 3 |

≥70% | 4 |

≥80% | 5 |

≥90% | 6 |

### Registration

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