University of Cambridge > Talks.cam > Category Theory Seminar > Betweenness reals: How to do Dedekind cuts when you don't know which way is up

Betweenness reals: How to do Dedekind cuts when you don't know which way is up

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Recently Vaughan Pratt claimed on the categories list that any of the standard constructions of the reals from the rationals could be carried out using only the affine-space structure of the rationals. As I pointed out at the time, that is not quite true, because the Dedekind-cuts construction makes essential use of the order-relation on Q, which is not definable from the affine structure since Q has order-reversing affine automorphisms. However, Q does have a ternary ‘betweenness’ relation definable from its affine structure. In this talk I shall investigate how the Dedekind-cuts construction can be made to work for spaces equipped with a betweenness structure: the results are mostly predictable, but there are one or two unexpected twists.

This talk is part of the Category Theory Seminar series.

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