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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | 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
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Reading List
Keith Devlin, The Joy of Sets - Springer(free on-line access available)
Patrick Suppes, Axiomatic Set Theory - Dover, QA248Sup.
Thomas Jech, Set Theory- Springer, QA248Jec. (and free on-line access)
William Lawvere, Robert Rosebrugh, Sets for Mathematics - CUP, QA248Law (and free on-line 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 |
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