The Distance Function on a Computable Graph

Details The Distance Function on a Computable Graph The Distance Function on a Computable Graph

2011-11-10

arxiv.org/abs/1111.2480v1

Mathematics

Logic

submitted for publication 9 November 2011

Scientific paper

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove assorted theorems about the new reducibilities and about functions which have nonincreasing computable approximations. Finally, we show that the spectrum of the distance function can consist of an arbitrary single btt-degree which is approximable from above, or of all such btt-degrees at once, or of the bT-degrees of exactly those functions approximable from above in at most n steps.

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