Gödel's Incompleteness Theorems, Spring 2015

This course is part of the Mastermath programme.
Lecturer is Jaap van Oosten. Exercise classes are given by Jetze Zoethout (J.Zoethout@uu.nl).

This course will be given in weeks 6-21 (February-June 2015).
The course is on Mondays, 14:00-16:45, in Utrecht
The course will be concluded by a written exam. There are, during the course, 6 hand-in exercises, which may count for 30% of your final grade (it is not compulsory, although strongly recommended, to hand in these exercises). That is, your final grade will be calculated as follows: let H be your grade for the hand-in exercises and W your grade for the written exam. Your final grade will be the maximum of W and the number (3H + 7W)/10.
The hand-in exercises have to be handed in at the exercise class in the week they are mentioned below.
Here are model solutions for the hand-in exercises. These will appear a week after they were due.

Literature: We use Lecture Notes for the course. A printed and bound copy of the lecture notes is available at the A-Eskwadraat bookstore, Buys Ballot Building, second floor. Payment by bank card.

Overview of the material treated in the course

• Week 6: Introduction: some history and philosophy, Hilbert's Programme. Conservative and definitional extensions of theories; omitting types theorem. Exercises: 18--21.
• Week 7: Primitive Recursive Functions. Chapter 3, pp.33--42. Exercises: 24 vi)--ix), 27, 32.
• Week 8: Partial Recursive Functions: remainder of Chapter 3. Exercises: 37,43,44,47. Hand-in Exercise: exercise 38 of the lecture notes.
• Week 9: Last bits of Chapter 3. The formal System PA (1). Exercises: 48,49,51,53,55.
• Week 10: The Formal System PA (2). Exercises: 56,58,59,60,63. Hand-in Exercise:Exercise 2
• Week 11: The Formal System PA (3). Exercises: 59,60,61,67,68.
• Week 12: Gödel Incompleteness (1). Exercises: 72,73,75,76. Hand-in Exercise:Exercise 3
• Week 13: Gödel Incompleteness (2). Exercises: 77,78,80,81,82.
• Week 14: Introduction to Models of PA (1). Sections 6.1--6.3. Exercises: 84,85,87,90,91,94. Hand-in Exercise:Exercise 4
• Week 15: No lecture on April 6: Second Easter Day.
• Week 16: Introduction to Models of PA (2). Exercises: 92,93,95,96. Hand-in Exercise:Exercise 5
• Week 17: Introduction to Models of PA (3). Prime models and McDowell-Specker. There are no exercises in this section; students can catch up with old exercises.
• Week 18: No Lecture on April 27: King's Day (National Holiday)
• Week 19: Recursive Aspects of Models of PA (1). Section 7.1. Exercises: 97,98,99,101,102. Hand-in Exercise:Exercise 6
• Week 20: Recursive Aspects of Models of PA (2).
• Week 21: Recursive Aspects of Models of PA (3).
• Week 22: No lecture on May 25: second Whitsun (Pentacosta) Day.
• Week 23: Exam, Thursday June 4, 10-13, Educatorium room Alpha Here is the exam, with solutions.
  Old exam, with some solutions. Another one. Another one (without solutions).
• Week 26: Resit, Thursday June 25, 10-13, BBG room 201. Here is the retake exam, with solutions.

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