Undergraduate Course: Axiomatic Set Theory (MATH11236)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Year 5 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  A first course in axiomatic set theory to include ordinals, cardinals, the axiom of choice developed in the axiom system chosen by the lecturer 
Course description 
Paradoxes in nineteenth century mathematics showed that there is a need to be precise about the foundations of mathematics. Set Theory provides such a foundation. It also provides ways to deal with notions of infinity (through ordinal and cardinal numbers). The course will explore one or more such axiomatic formulations of Set Theory and show how to develop mathematics from these axioms as well as extensions of mathematics through ordinal and cardinal arithmetic. It will look at the axiom of choice and equivalents. Further topics may include model theory, large cardinals and/or independence proofs.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Demonstrate key consequences of an axiom system for Set Theory
 Demonstrate cardinal and ordinal arithmetic skills
 Demonstrate how mathematics can be developed from the axioms
 Show how the Axiom of Choice and its equivalents are used in Mathematics

Reading List
Keith Devlin, The Joy of Sets  Springer(free online access available)
Patrick Suppes, Axiomatic Set Theory  Dover, QA248Sup.
Thomas Jech, Set Theory Springer, QA248Jec. (and free online access)
William Lawvere, Robert Rosebrugh, Sets for Mathematics  CUP, QA248Law (and free online access) 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  AST,Set Theory,Foundations 
Contacts
Course organiser  Prof Antony Maciocia
Tel: (0131 6)50 5994
Email: A.Maciocia@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

