# Unit information: Logic in 2019/20

Please note: Due to alternative arrangements for teaching and assessment in place from 18 March 2020 to mitigate against the restrictions in place due to COVID-19, information shown for 2019/20 may not always be accurate.

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Unit name Logic MATH30100 20 H/6 Teaching Block 2 (weeks 13 - 24) Dr. Fujimoto Not open MATH10004 Foundations and Proof and MATH10005 Introduction to Group Theory (or MATH10010 Introduction to Proofs and Group Theory) MATH10003 Analysis 1A and MATH10006 Analysis 1B (or MATH10011 Analysis) None School of Mathematics Faculty of Science

## Description

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 Philosophy of Mathematics.

## Intended learning outcomes

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.

## Teaching details

Lectures and problems classes.

## Assessment Details

100% Examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

## Reading and References

Recommended

• Heinz-Dieter Ebbinghaus, Jörg Flum, and Wolfgang Thomas, Mathematical Logic, Springer, 1994
• Herbert Enderton, A Mathematical Introduction to Logic, Academic Press, 2001