# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

### Timetable information in the Course Catalogue may be subject to change.

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Axiomatic Set Theory (MATH11236)

 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.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None
 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
 Not being delivered
 On completion of this course, the student will be able to: Demonstrate key consequences of an axiom system for Set TheoryDemonstrate cardinal and ordinal arithmetic skillsDemonstrate how mathematics can be developed from the axiomsShow how the Axiom of Choice and its equivalents are used in Mathematics
 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)
 Graduate Attributes and Skills Not entered Keywords AST,Set Theory,Foundations
 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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