Axiomatic Set Theory: MT 2003


A course synopsis may be found on the departmental webpages, or in a booklet available from the Mathematical Institute.


The material in b1 set theory, logic and further logic will be assumed.


Goldrei's Classic Set Theory contains much of the material; Kunen's Set Theory: An introduction to independence proofs contains all of it and a great deal more besides; including a proof that if ZF is consistent, then the Continuum Hypothesis cannot be proved from ZFC. Devlin's Constructibility contains more about Gödel's Constructible Universe.

Problem sheets

These are available in postscript or pdf format.


The first handout (postscript/pdf) includes the axioms of set theory and definitions of basic set theoretic operations, most of which will be familiar from b1. It also includes an outline of the strategy that will be adopted in this course of lectures, in proving consistency theorems in set theory.

The second handout (postscript/pdf) contains material on absoluteness, including a list of formulae that are absolute between transitive models of set theory.

The third handout (postscript/pdf) gives the formalities of the Definable Power Set operation: an important ingredient in Gödel's Constructible Universe. A less formal treatment is given in the lectures.

Research opportunities

In Britain, one can do research in set theory at UEA or Bristol, for instance.

Ex-Oxford people can be found at Bonn and Berlin. But worldwide, there is an enormous amount of set theory in the USA and Israel. There is an important group at Berkeley.

Charles Morgan's homepage has a wide variety of set-theory related links.

Enquiries about studying logic in Oxford could be directed to Prof. Wilkie or Prof. Zil'ber of the Oxford Logic Group.

This page last modified by R. W. Knight
30 October 2002
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