On n-dependent groups and fields

Nadja Hempel (1)

1 ICJ - Institut Camille Jordan

First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IPn property for all natural numbers n and certain properties of dependent (NIP) valued fields extend to the n-dependent context.

Mots clés: Artin-Schreier extensions; n-dependent fields; n-dependent groups

Domaines: Logique [math.LO]

Nadja Hempel. On n-dependent groups and fields. 2014. ⟨hal-00933339v2⟩