To teach the fundamentals of mathematical logic.
The course covers the basic model theory and proof theory of 1st order languages, the Gödel Completeness Theorem and the Godel Incompleteness Theorems characterising the non-provability of the consistency of a formal system within that system. These theorems are the foundations of 20th century logic.
Relation to other units
Logic is a prerequisite for Axiomatic Set Theory. It is essential for an understanding of much of the foundations of mathematics but is not restricted to that. In particular it is essential for much of analytical philosophy.
It is of particular interest to students taking the joint Mathematics and Philosophy degrees, or the MA in Philosphy of Mathematics
After taking this unit, students should be familiar with the basic principles of first order logic and should understand the technique of arithmetisation of syntax which underlies the proofs of the Gödel Incompleteness Theorems.
Assimilation and use of novel and abstract ideas.
- Truth-functional Logic
- Canonical Models
- First Order Logic
- Proof Systems
- Gödel's Completeness Theorem
- The Gödel's Incompleteness Theorems
Reading and References
Course notes will be supplied.
Unit code: MATH30100
Level of study: H/6
Credit points: 20
Teaching block (weeks): 2 (13-24)
Lecturer: Dr Kentaro Fujimoto
MATH10004 Foundations and Proof, MATH10003 Analysis 1A, MATH10006 Analysis 1B, and MATH10005 Introduction to Group Theory
Methods of teaching
Lectures supported by homeworks.
Method of Assessment
The pass mark for this unit is 40.
The final mark is calculated as follows:
- 100% from a 2 hour 30 minute exam in May/June
NOTE: Calculators are NOT allowed in the examination.
For information resit arrangements, please see the re-sit page on the intranet.
Further exam information can be found on the Maths Intranet.