Module and Programme Catalogue

Search site

Find information on

2008/09 Undergraduate Module Catalogue

MATH3102 Mathematical Logic 2

15 creditsClass Size: 100

Module manager: Professor S. B. Cooper
Email: S.B.Cooper@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2008/09

Pre-requisites

MATH2040Mathematical Logic 1

This module is mutually exclusive with

MATH5102MAdvanced Logic

This module is approved as an Elective

Module summary

Metamathematics and proof theory try to answer fundamental questions about axiomatic theories (e.g. number theory) like: Are they consistent (free from contradiction)? How do we know? Could they be developed by computers without human assistance? (answer: no) Are mathematicians necessary? (answer: yes). The main goal is to prove Godel's Incompleteness Theorems (1931) which show that if a formal theory has strong enough axioms then there are statements which it can neither prove nor refute.

Objectives

To develop fundamental concepts and techniques of Mathematical Logic sufficient to prove Godel's Incompleteness Theorems, and to relate them to notions of computability, decidability and undecidability. To enable students to understand and write formal proofs in logical style. On completion of this module, students should be able to:
a) carry out elementary proofs in first-order formal logic and Peano Arithmetic;
b) prove representability and recursiveness of basic number-theoretic functions and relations;
c) understand and reproduce proofs of Godel's Incompleteness Theorem for predicate logic, Godel's Incompleteness Theorems for Peano Arithmetic, Lob's Theorem and related results;
d) describe connections between incompleteness, consistency, computability and undecidability;
e) show a capacity for independent study, including further development of the theory via a range of more challenging homework problems.

Syllabus

Revision of first-order logic including Godel's Completeness Theorem; the axiomatic method and formal Peano Arithmetic; recursive functions and representability; the arithmetization of syntax and Godel's First Incompleteness Theorems; Lob's Theorem and the Second Incompleteness Theorem; consistency, undecidability and computability.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Example Class71.007.00
Lecture261.0026.00
Private study hours117.00
Total Contact hours33.00
Total hours (100hr per 10 credits)150.00

Methods of assessment


Exams
Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)3 hr 100.00
Total percentage (Assessment Exams)100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 24/07/2009

Disclaimer

Browse Other Catalogues

Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD

© Copyright Leeds 2013