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We construct a computable vector space with the trivial computable automorphism group but with a complicated dependence relation. Thus, we answer a question asked by A. Morozov in [6].

Cohesive sets play an important role in computability theory. Here we use cohesive sets to build nonstandard versions of the rationals. We use Koenigsmann's work on Hilbert's Tenth Problem to establish that these nonstandard fields are rigid. As a consequence we obtain results about automorphisms of the lattices of computably enumerable vector spaces… (More)

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