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    The conjugacy problem for automorphism groups of countable homogeneous structures

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    We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility

    Bowtie-free graphs and generic automorphisms

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    We show that the ω\omega-categorical existentially closed universal bowtie-free graph of Cherlin-Shelah-Shi admits generic automorphisms in the sense of Truss. Moreover, we show that this graph is not finitely homogenisable.Comment: 14 page
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