6 problems

The theory $ACFA_p$ denotes the theory of existentially closed difference fields of characteristic $p>0$. The $\b5$-existence property over the fixed field asks whether every $\b5$…

Let $H_{\mathrm{KP}}$ be the identity component of the Kim–Pillay group associated with the theory $\mathrm{ACFA}^{+}$, the amalgam of $\mathrm{ACFA}$ and $\mathrm{PF}^{+}$. Hrusho…

Let $K$ be a pseudofinite difference field of the form … Here $DF(p_i,n_i,m_i)$ denotes the finite difference field factors, and assume that $n_i$ grows sufficiently faster than…

A pseudofinite difference field carries an integer-valued dimension coming from the non-standard counting size of definable sets. For a quantifier-free definable set, let its trans…

Let $(F,\operatorname{Frob})\in\mathcal{S}$. For any countable set $A\subseteq F$ and complete quantifier-free $\mathcal{L}_\sigma$-type $p(x)\in S^{qf}_n(A)$, the two dimensions a…

Finite-rank conjecture. Suppose that $p_1$ is minimal in the sense of $L_1$ and ACFA. If $p_1$ is grouplike in the sense of $L_1$ and ACFA, then $p$ has finite rank in the sense of…