# Logic

## Unit aims

To teach the fundamentals of mathematical logic.

## Unit description

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

## Learning objectives

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.

## Transferable skills

Assimilation and use of novel and abstract ideas.

## Syllabus

1. Truth-functional Logic
2. Canonical Models
3. First Order Logic
4. Proof Systems
5. Gödel's Completeness Theorem
6. 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

## Pre-requisites

MATH10004 Foundations and Proof, MATH10003 Analysis 1A, MATH10006 Analysis 1B, and MATH10005 Introduction to Group Theory

None

## 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.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.