I am getting quite a lot of hits from you out there, but I don't
know what you are looking for. (I have just the one counter on this
top page.) If you find any of my documents useful,
please let me know. I spend a fair amount of my time writing new sets
of notes which eventually I hope to make publically
available. Information from you will give me an indication of which
documents you find most useful, and hence what I should concentrate on
in the future. Thank you.
I am a mathematician with fairly broad research interests, mostly in
the area of mathematical logic. In my time I have worked in decisions
problems, model theory, lattice theory, point-free (and
point-sensitive) topology, category theory, ring theory and sheaf
representations, recursion theory, $\lambda$-calculus, and proof
theory, with varying degrees of failure.
From 1965 to 1996 I was employed as a mathematician in various
universities. In 1996 I took early retirement in order to become a
full time academic and do something useful. I now spend my time
helping to teach research students and writing various documents which
I think may be useful to the mathematical community. Occasionally I
published these via the more traditional routes, but these days I
prefer to make them available via the web, because:
I don't need the brownie points (and I am less than impressed by some
of the things brownie points are awarded for these days);
the refereeing process has become appalling, and it is hardly
worth the effort putting up with some of the crap;
I am sick of commercial publishers shafting the mathematical
These pages contain documents of various kinds which I have divided
into the several categories. At the moment not all of these documents are
If you find, or would find, any of these documents useful,
please let me know (along with any suggestions for improvement). I
have a hit counter at the bottom of this page which started operating
in January 2002. Currently I am getting something between three and
four hits per day. I don't know where most of these have come
from, but clearly some have been looking for documents of various
kinds. It would be nice to know which documents you find most
valuable, so I can concentrate on writing that kind of material.
20th century publications
There is a complete
list of my publications
mostly papers but with one or two books. Of course most of these are
not available in electronic form (unless you can go directly to the
There is a list of
to the book Derivation and Computation.
Papers and Notes
The difference between a Paper and a set of Notes is not absolutely clear.
In general a Paper tends to be shorter and rather tersely written.
Some of the papers have been been published or submitted for
publication. Others I will simply leave here,
at least for the time being.
A set of Notes is more expansive and usually longer. However,
sometimes such notes are quite short (and written because I couldn't
find a self contained account of the topic).
Sometimes a Paper contains material that is `well known' and
therefore doesn't deserve to be published in a respectable
journal. Sometimes a set of Notes contains material that is quite
new, and perhaps could be turned into a journal paper.
Where available, after each abstract there are links to various forms
of that document.
Seminar and talks
Over the years I must have given hundreds of seminars, talks, and
short research courses. Recently I started to keep a record of these
together with various associated documents. These are listed in
together with abstracts of some of the talks and links to relevant
documents (slides and notes) where available.
Rosi Sexton on Point-free Topology
Between 1999 and 2003 Rosi Sexton wrote her MSc Dissertation and PhD
Thesis under my supervision. Both centred around a point-free
analysis of the patch construction in point-set topology. Follow this
for links to both these documents and to version of two papers arising out
of this work.
A collection of notes on frames
Various sets of notes on frames (complete heyting algebras viewed as
algebraic analogues of topologies).
This collection is in production but some are already available.
These are longer documents some of which are genuine
books intended for publication (if the publishers buy me enough
drink, for the buggers will never pay enough for the amount of
work involved). Some of these
are fairly well developed,
others are quite some way from being finished. Consequently, there
are links to only some of these documents.
Notes, slides, and other material for a course given over the grid.
Mathematics and Computation
The MFG runs a 30 hour lecture course
Mathematics and Computations as part of a taught
MSc in Mathematical Logic. An overview of that course can be found at
These are documents that are in the process of
production (and some have been for several years). Some of them are
partly in electronic form and some merely hand written. However, at
the moment none of them are in a fit state to be let loose in the
I will write more details for this block in due course.
Room 2.120A in the Computer Building, Manchester University, Oxford
Road, Manchester M13 9PL, England.
Telephone: +44 161 275 6288
This page is maintained by myself, email address above. Last