Course details
A core MAGIC course
Semester
 Autumn 2018
 Monday, October 8th to Friday, December 14th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Thursdays
 15:05  15:55
Description
This course is an introduction to set theory, focusing on foundational issues but with an eye also on the study of combinatorial properties of infinite objects.
We will start by motivating and introducing ZFC. Then we will develop the basic theory of the ordinals and cardinals in this theory, and will prove some classical theorems of combinatorial flavour. Possible topics may include cardinal arithmetic, Aronszajn trees, infinite Ramsey theory and/or some results on determinacy of games. Time permitting, I will briefly discuss large cardinal axioms, the independence phenomenon, and the problem of finding natural extensions of ZFC.
One of the goals of the course is to engage a working mathematician into looking at the foundations of the mathematical building.
Prerequisites
There are no prerequisites for this course, except for a reasonable level of mathematical maturity. Having been exposed to a course in mathematical logic would be desirable but not necessary. I will in fact give brief introductions to the relevant notions from logic.
Syllabus
Naive set theory: Sets as foundational framework for mathematics. Paradoxes.
Axiomatic set theory: ZFC.
Ordinals and cardinals. Transfinite recursion and induction. The cumulative hierarchy.
Countable and uncountable sets.
The Axiom of Choice.
Basic cardinal artihmetic.
Some combinatorial set theory: Aronszajn trees, infinite Ramsey theory.
Determinacy of infinite games.
Large cardinal axioms: Weakly compact, measurable, and beyond.
Natural axioms for mathematics: Extending ZFC.
Lecturer

DA
Dr David Aspero
 University
 University of East Anglia
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library'  this sometimes works well, but not always  you will need to enter your location, but it will be saved after you do that for the first time.
 Set theory: an introduction to independence proofs (Kenneth Kunen, book)
 Set Theory: The Third Millenium Edition, Revised and Expanded (Thomas Jech, )
 A mathematical introduction to logic (2nd. edition) (Herbert Enderton, )
Assessment
Description
There will be a takehome exam at the end of the course. The questions will be posted shortly after the end of the lecture period. Solutions may be submitted as scanned pdf's.
Assessment not available
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Lectures
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