Breadcrumb

Logic (MATH 30100)

Academic Year:

Contents of this document:

Administrative Information

  1. Unit number and title: MATH 30100 Logic
  2. Level: H/6
  3. Credit point value: 20 credit points
  4. Year: 12/13
  5. First Given in this form: 1991
  6. Unit Organiser:
  7. Lecturer: Dr Kentaro Fujimoto (also the unit Organiser)
  8. Teaching block: 2
  9. Prerequisites: Normally: the 1st Year Pure Maths units (or an equivalent): MATH11511 Number Theory & Group Theory, MATH11006 Analysis 1 and MATH 11521 Further Topics in Analysis

Unit aims

To teach the fundamentals of mathematical logic.

General Description of the Unit

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 20'th century logic. 

Relation to Other Units

Logic is a prerequisite for the Level 7 unit 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 

 

Teaching Methods

Lectures and problems classes.

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.

Assessment Methods

The final assessment mark for Logic is calculated from a 2 ½ -hour written examination in May/June consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators are NOT permitted be used in this examination.

Award of Credit Points

Credit points are gained by:

  • either passing the unit,
  • or getting an examination mark of 30 or over, and also making satisfactory attempts at selected homework questions.

Transferable Skills

Assimilation and use of novel and abstract ideas.

Texts

Course notes will be supplied.

 

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

Unit Organiser

Dr Kentaro Fujimoto
School of Mathematics, University of Bristol