# Harold Simmons

### Welcome to my homepage

These pages are in the process of fabrication.

00-IDSandMODS .

SetTheory .

FOR-TOMMY .

#### Information

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.

#### Research Interests

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.

#### Vocation

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 community.

#### Documents

These pages contain documents of various kinds which I have divided into the several categories. At the moment not all of these documents are available electronically. 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 publishing journal).

There is a list of corrections 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.

A list of titles and abstracts of these documents is given in Papers-and-Notes.

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 Seminars 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. Rosi.

#### A collection of notes on frames

Various sets of notes on frames (complete heyting algebras viewed as algebraic analogues of topologies). Frames. This collection is in production but some are already available.

#### Books

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 Books are fairly well developed, others are quite some way from being finished. Consequently, there are links to only some of these documents.

#### Model Theory, MSc course, Feb and March 08

Material for the course can be found here. Model-Theory

#### Category Theory by Magic

Notes, slides, and other material for a course given over the grid. Magic-Cats

#### 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 overview.dvi or overview.pdf or overview.ps .

That course consists mainly of introductions to Category theory using the notes CatTheory.dvi or CatTheory.ps.gz or CatTheory.pdf and to Lambda-calculi using the notes lcalculus.dvi or lcalculus.ps.gz or lcalculus.pdf . Both of these are in book form.

This block was last updated in February 06.

#### Ordinal Notations

By going to here Ordinal-Notations you will find several documents on that topic.

#### In Production

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 community.

I will write more details for this block in due course.

### Finding me:

• Room 2.120A in the Computer Building, Manchester University, Oxford Road, Manchester M13 9PL, England.
• e-mail: hsimmons@manchester.ac.uk
• Telephone: +44 161 275 6288