Let E be a field, G a finite group, and G i| i∈ I a finite set of subgroups of G with G=< G i| i∈
I>. For each i∈ I we are given a Galois extension F i of E with Galois group G i. We suggest …

GENERIC DERIVATIONS ON ALGEBRAICALLY BOUNDED STRUCTURES T : the expansion
of T saying that the i are derivations which commute w Page 1 The Journal of Symbolic Logic …

Let K be a field. The étale open topology on the K-points V (K) of a K-variety V was
introduced in [23]. The étale open topology is non-discrete if and only if K is large. If K is …

Let K be an algebraically bounded structure. If K is model complete, then the theory of K
endowed with a derivation has a model completion. Similar results hold for several …

We examine fields in which model theoretic algebraic closure coincides with relative field
theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For …

In [1], Anscombe and Koenigsmann give an existential∅-definition of the ring of formal
power series F [[t]] in its quotient field in the case where F is finite. We extend their method in …

Suppose that R is a local domain with fraction field K. If R is Henselian, then the R‐adic
topology over K refines the étale open topology. If R is regular, then the étale open topology …

We give a characterization, in terms of the residue field, of those henselian valuation rings
and those henselian valuation ideals that are diophantine. This characterization gives a …

Nondefinability of Rings of Integers in Most Algebraic Fields Page 1 Notre Dame Journal of
Formal Logic Volume 62, Number 3, 2021 Nondefinability of Rings of Integers in Most Algebraic …

We study subfields of large fields which are generated by infinite existentially definable
subsets. We say that such subfields are existentially generated. Let L be a large field of …