Abstract: 

I will talk about joint work with Jan Dobrowolski and Francesco Gallinaro on existentially closed valued difference fields, with no restriction imposed on the behaviour of the automorphism on the value group. We prove that such structures admit an equivariant section of the valuation, hence an equivariant angular component. In the language with such an angular component, assuming residue characteristic 0, we prove transfer of amalgamation of substructures from the residue field, characterise the existentially closed models, and deduce that they are NTP2 in the sense of positive logic.

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