**Credits** |
8 credit points |

**Instructors** |
Barendregt, H.P. (Radboud Universiteit Nijmegen), |

**E-mail** |
henk@cs.ru.nl, |

**Prerequisites** |
Some mathematical experience. |

**Aim** |
To understand one of the fundamental issues of metamathematics |

**Organization** |
The axiomatic method was described by Aristotle: mathematics consists of objects and properties. Objects can be obtained from primitive ones using definitions. Properties can be established from axioms using proofs. The Gödel first incompleteness theorem states that contradiction free axiomatic systems as least as strong as arithmetic are incomplete. This means that there are statements A that can neither be proved nor be refuted. The second incompleteness theorem states that, although consistency can be formulated in systems as least as strong as arithmetic, this statement is among the undecided ones. In spite of this the axiomatic method is all we have and it is quite powerful. |

**Examination** |
Written exam: May 26, 14:00-17:00h. Science Park C0.110. Some extra tests will be given that can increase but cannot decrease the final mark. |

**Literature** |
Lecture notes can be downloaded here. |

**Remarks** |
More information you can find here. |