# Axiomatic Set Theory: MT 2003

## Synopsis

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

## Prerequisites

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

## Reading

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.

## Handouts

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

Email corrections and comments to
*knight@maths.ox.ac.uk*