Dependence relations in computably rigid computable vector spaces

Abstract. We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Turing degrees. As a corollary, we answer a question asked by A. Morozov in [7]. The authors are very thankful to the referee for important suggestions. The last two authors also acknowledge support of the NSF binational grant DMS-0075899.

• Type: Journal
• Year: 2005
• Where: APAL
• Authors: Rumen D. Dimitrov, Valentina S. Harizanov, Andrei S. Morozov
• Keywords: APAL 2005, Computable Vector Space, NSF Binational Grant, Trivial Computable Automorphism