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##### Mathematical Proceedings of the Cambridge Philosophical Society

**Aims and scope**

Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.

**Submission of manuscripts**

Papers should be submitted electronically to the Editor at mpeditor@hermes.cam.ac.uk in pdf form only.

Papers in languages other than English should be sent only after prior consultation with the Editor, who may be contacted at the e-mail address above.

When a paper has been accepted for publication the relevant TeX files of the final version, accompanied by a pdf file, should be sent to the Editor by e-mail.

The class file, together with a guide, PSP2egui.tex, and sample pages, PSP2esam.tex, can be downloaded here.

These files will be updated periodically: please ensure that you have the latest version.

**Preparation of manuscripts**

Authors are strongly encouraged to prepare their manuscripts in LaTeX 2e using the PSP class file.

Papers produced in the recommended way can be printed directly from author-prepared electronic files: this substantially reduces errors at the printers. While the use of the PSP class file is preferred, other LaTeX or plain TeX files are also acceptable. In case standard electronic preparation is impossible papers may be typed, double-spaced, on one side of white paper (of which A4, 210 by 297mm, is a suitable size). The pages must be numbered. Margins of 30mm should be left at the side and bottom of each page.

A cover page should give the title, the author's name and institution, with the address to which mail should be sent.

The title, while brief, must be informative (e.g*. A new proof of the prime-number theorem*, whereas, *Some **applications of a theorem of G. H. Hardy *would be useless).

Authors are asked to provide an abstract as a basis for a search on the Web. This may be an explicit abstract at the start of the paper. Otherwise the first paragraph or two should form a summary of the main theme of the paper, providing an abstract intelligible to mathematicians. Please note that the abstract should be able to be read independently of the main text. References should therefore not be included in the abstract.

Authors are encouraged to check that where references are given, they are used in the text. Experience has shown that unused references have a habit of surviving into the final version of the manuscript.

**Layout of manuscripts**

For a typescript to be accepted for publication, it must accord with the standard requirements of publishers, and be presented in a form in which the author's intentions regarding symbols etc. are clear to a printer (who is not a mathematician).

The following notes are intended to help the author in preparing the typescript. New authors may well enlist the help of senior colleagues, both as to the substance of their work and the details of setting it out correctly and attractively.

Please also check the Cambridge University Press website for information about the style in which the paper should be submitted.

**Notation**

Notation should be chosen carefully so that mathematical operations are expressed with all possible neatness, to lighten the task of the compositor and to reduce the chance of error.

For instance *n *sub *k *is common usage, but avoid if possible using *c *sub *n *sub *k*. Fractions are generally best expressed by a solidus. Complicated exponentials like:

$ \exp\{z^2\sin\theta/(1 + y^2)\} $

should be shown in this and no other way.

It helps if displayed equations or statements which will be quoted later are numbered in order on the right of their line. They can then be referred to by, for example ‘from (7)’.

The author must enable the printer (if necessary by pencilled notes in the margin) to distinguish between similar symbols such as *o*, *O*, o, O, O; *x*, X, \times$; $\phi, \Phi, \emptyset$; l, 1, $\varepsilon, k, $\kappa, k$.

Footnotes should be avoided.

Please use typewriter fount for all addresses and email addresses.

Omit □ from the end of proofs.

In listing assertions, conclusions, etc. do not use a vertical column of dots and do not follow (a) or (i) by a capital letter (eg. (i) the absolute value...)

In making references precise use [3, theorem 5.1]

**Diagrams**

Diagrams should be in black ink or from a high-quality laser printer and should not be larger than 30 cm by 45 cm. Lettering to be inserted by the printer should be shown clearly on copies of the figures rather than on the original drawings. Please note that a charge may be made if hand-drawn diagrams need to be redrawn for publication.

Figure 1 here

A typed list of captions may be provided at the end of the manuscript in the following format:

Figure 1. *A basis for…*

Note that there is no point at the end of the heading. All headings should be centred.

**Tables**

Tables should be numbered (above the table) and set out on separate sheets. Indicate the position of each in the text as for figures:

Table 3 here

Headings for tables should be shown in the following way:

Table 3. *A basis for…*

Note that there is no point at the end of the heading. All headings should be centred over columns.

**References**

References should be collected at the end of the paper numbered in alphabetical order of the authors’ names. Where references are given, they should be used in the text. Titles of journals should be abbreviated as in *Mathematical Reviews*. The following examples show the preferred style for references to a paper in a journal, a paper in a proceedings volume, a book and an unpublished dissertation:

[**1**] J. F. ADAMS. On the non-existence of elements of Hopf invariant one. *Ann of Math*. (2) **72 **(1960), 20-

104.

[**2**] M. P. FOURAM and D. S. SCOTT. Sheaves and logic. *In Applications of Sheaves *Lecture Notes in Math.

vol. 753 (Springer-Verlag, 1979), pp. 302-401.

[**3**] P. T. JOHNSTONE. *Stone Spaces*. Cambridge Studies in Advanced Math. no. 3 (Cambridge University

Press, 1982).

[**4**] F. W. LAWVERE. Functional semantics of algebraic theories. PhD. thesis. Columbia University (1963).

*(Revised 26/03/2018)*