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For a fixed countably infinite structure Γ with finite relational signature τ , we study the following computational problem: input are quantifier-free τ-universal quantification are forbidden). We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure ∆ with a finite relational… (More)

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form L p∈I Z(p ∞), where I is an infinite set of primes.

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