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Final report: http://images.xeny.net/jason/d/187-1/Taylor+-+Computable+reals+and+constructible+sets.pdf

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Notes:

http://en.wikipedia.org/wiki/Ordinal_number#Transfinite_induction

Normal J. Wildberger:
- http://web.maths.unsw.edu.au/~norman/papers/Ordinals.pdf

Paradoxes of naive set theory — basically only three? (Philosophers argue a lot about what counts as a set-theoretic paradox and what counts as a "semantic" paradox.)
- Cantor's paradox: 187?, the largest cardinal
- Burali-Forti's paradox: 1897?, the largest ordinal
- Russell's paradox: the set of sets that are not members of themselves, 1900

Questions to follow up

None of these compulsory (i.e. do none or more):
- Are Wildburger's infinitesimals helpful with the original problem about Cantor's infinities not being fine-grained enough?
- How are other types of infinitesimal related to Wildburger's? Are they more helpful?
- Do alternative set theories look like they might be helpful? See
http://plato.stanford.edu/entries/settheory-alternative/
http://plato.stanford.edu/entries/quine-nf/
- The author of the latter page will be in Australia briefly after our next meeting, so maybe think of questions to ask him.

Alternative Set Theory:
- Pure sets are constructed by induction
- Automatically avoids the paradoxes
- Is simple and doesnt rely on 9 axioms
- Similar in many ways to Wildberger's set-up and also to hyperreals, and natural numbers

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Additional topic 3 September: internal and external proofs; e.g. applications of http://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem

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Computable reals:
http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf