Degrees of convex dependence in recursively enumerable vector spaces

Thomas A. Nevins

Research output: Contribution to journalArticlepeer-review

Abstract

Let W be a recursively enumerable vector space over a recursive ordered field. We show the Turing equivalence of the following sets: the set of all tuples of vectors in W which are linearly dependent; the set of all tuples of vectors in W whose convex closures contain the zero vector; and the set of all pairs (X, Y) of tuples in W such that the convex closure of X intersects the convex closure of Y. We also form the analogous sets consisting of tuples with given numbers of elements, and prove similar results on the Turing equivalence of these.

Original languageEnglish (US)
Pages (from-to)31-47
Number of pages17
JournalAnnals of Pure and Applied Logic
Volume60
Issue number1
DOIs
StatePublished - Feb 24 1993

ASJC Scopus subject areas

  • Logic

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