Appendix 1Mathematical background

In this appendix we collect together some useful mathematical background. Readers may prefer to read the main text and refer to this appendix only if they get stuck. We do not give much in the way of proofs and the style is terse and rather dull, so this is not a substitute for standard texts. For example, Forster (2003) discusses in detail almost all the topics here, as well as much relevant material in logic and computability and some more advanced topics in set theory.

**Mathematical notation and terminology**

We use ‘iff ’ as a shorthand for ‘if and only if ’ and ‘w.r.t.’ for ‘with respect to’. We write *x* | *y* , read ‘*x* divides *y*’, to mean that *y* is an integer multiple of *x*, e.g. 3 | 6, 1 | *x* and *x* | 0. We ...

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