… In this paper we show that fields with a (Q, +)-action are far more tame. … of L1 and ACFA,
then p is orthogonal to all Lq-definable minimal fields in the sense of Lq and ACFA for all q ∈ Q. …

… 公理系 ACFA の存 在する理由としては, 代数的閉体上のイデアルの既約性がイデアルを生成
する多 項式の係数の性質として言語 $\mathcal{L}$ で記述できることが本質的である. モデル完全な…

… the theory of fields with a generic automorphism, ACFA, which is a theory of model companion
of … a model companion of the theory of iterative $q$-difference fields of characteristic zero. …

… [4], which estimates the score of affinity between consumer p and product q, denoted as \(x_{pq}\),
by their connections … We report the performance of CFA and ACFA in these settings. …

… Once the above problem is solved, we can characterize the \((f_i,a_i)\)’s so that the \(\hat{h}_{f_i}(a_i)\)’s
are linearly dependent over \({\mathbb Q}\) without the further local conditions of …

… Then we have Q ⊂ Q and one can identify Galδ( Q/ K) with a subgroup of Gal(Q/ K) by
restricting the elements of Galδ( Q/ K) to Q. The following result provides a fundamental link …

… In the case k = Q we recover the usual notions of derivations and endomorphisms. The …
axioms for ACFA in [7]. The morphism ˆπ0 is the projection to X, and ˆπ1 is the projection to Xσ. …

… In the future, we aim to investigate whether some of the results that hold in ACFA could be …
For example, if \(a, b \in {\mathbb {Q}}\), then we can write a formula \(\phi (x,y) \in {\mathcal {E}}…

… q)\) the corresponding twisted simple group over \({\mathbb {F}}_q\). (Here we are using the
notation q rather than \(q… We claim that for infinitely many powers q of p we have \({\mathbb {F…

… The theory of difference fields, expressed in the first-order language of rings expanded by a
unary function symbol for the endomorphism, admits a model companion, ACFA, the models …