MAGIC050: Set Theory

Course details

A core MAGIC course


Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th


Live lecture hours
Recorded lecture hours
Total advised study hours


12:05 - 12:55


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.


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.


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.


  • DA

    Dr David Aspero

    University of East Anglia


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The assessment for this course will be released on Monday 7th May 2018 and is due in by Sunday 20th May 2018 at 23:59.

There will be a take-home exam at the end of the course. The exam questions will be announced right after the end of the teaching term. You will be able to send your answers as a pdf before the end of the exam period. All details will be available at the end of the teaching term.

Please note that you are not registered for assessment on this course.


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