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Set theory:
See on an alternative to ZF …
and lots else all over the web on alternatives to the axioms of ZF.

- Any relationship between the maths of fractals and spacetime is good (i.e. is philosophical).
- Are coastlines etc. really fractal even though they obviously don't have the structure of any fractal set described in pure mathematics?
- Orderings on fractal sets.
- Fractals and computability (computation of fractal sets by machines more or less powerful than Turing machines). Relationship between ordering and computability.
- Something about the axiom of choice. (But maybe fractal stuff only needs the Axiom of Finite Choice, which is much easier to get in all the set theories we know.)

- Can we describe fractals over alternatives to ZF?

Brendan Harding - Ph B Course Summary