Mathematical Logic 2005

This course will take place in autumn 2005, period 2. Jan Smith will be the lecturer, Fredrik Lindblad will be course assistants.

Lectures so far & Other news

The exams are now corrected!

Fredrik will give the lecture on Thursday and solve problems from the exam December 2004.

Prenex forms 2.5.10, 2.5.11 are not included this year.

Don't forget to register for the exam, December 4 is the last day!

October 25. History of logic, foundations of mathematics.
October 27. Sections 1.1 and 1.2.
November 1. Section 1.3 and Natural deduction.
November 3. Section 1.5.
November 8. More section 1.5.Constructive semantics (pp. 157-158)
November 10. Predicate logic. Sections 2.1, 2.2 and 2.3.
November 15. Semantics of predicate logic 2.4. Peano structures 2.7
November 17. Natural deduction for predicate logic. Discussion of the proof of the Soundness Theorem; before you read this proof, be sure that you understand the soundness proof for propositional logic!
November 22. Intuitionistic semantics, the Brouwer-Heyting-Kolmogorov interpretation of the logical constants (section 5.1). Kripke structures.
November 24. Equality in ND and most of section 3.1 (the completeness theorem for predicate logic)
November 29. End section 3.1 and the compactness theorem, infinte vs. finite (chapter 3.2). Non-standard models of arithmetic.
December 1. Finishing the proof of completeness, beginning Gödel's incompleteness theorem (extra material).

The timetable can be found here. The exam is December 13 before lunch in the V-building.

We will use van Dalen: Logic and Structure as main text. A list of what sections which are required reading for the course can be found here.

Here is some extra material for the course. These are preliminary versions and may change somewhat during the course.

#	Content
1	A general overview of the foundations of mathematics.
2	Sections 1.1 and 1.2
3	Section 1.3 and Natural Deduction.
4	Section 1.5.
5	More section 1.5. Constructive semantics for propositional logic (pp.157-158).
6	Predicate logic. Section 2.1, 2.2 and 2.3.
7	Semantics for predicate logic (Section 2.4).
8	Peano structures section 2.7. Natural deduction for Predicate logic.
9	More predicate logic. Intuitionistic logic, section 5.2. Kripke semantics (extra material).
10	Equality in ND and most of section 3.1 (the completeness theorem for predicate logic).
11	End section 3.1 and the compactness theorem, infinte vs. finite (chapter 3.2). Prenex forms.
12	Arithmetic I, (extra material).
13	Arithmetic II, Gödel's incompleteness theorem (extra material).
14	Exercises relevant for the exam, some of which you get here.

Tutorial sessions are held Thursdays 13.15-15.00 in vö11.

#	Content	Solutions
1	1.1: 3, 9; 1.2: 1b, 2a-c	pdf-file
2	1.4: 1a,b,c,f, 2a,c, 3b,d, 5; 1.6: 1; 1.5: 1, 2, 3, 7, 8, 9	pdf-file
3	1.4: 2, 4; 1.6: 4, 7	pdf-file
4	2.2: 1(i)-(iii); 2.3: 1, 2, 4d,f,g,h; 2.4: 1, 4, 5, 7	pdf-file (updated 2004-12-08)
5	2.7: 4; 2.9: 1, 3; Kripke notes: 1, 2a,b	pdf-file
6	3.1: 1, 3, 4; 3.3: 10	pdf-file
7	Exam problems from previous year.

Older exams (the course didn't cover exactly the same material):

Last updated: January 2, 2006.