We prove a categoricity transfer theorem for tame abstract elementary classes. Theorem 0.1. Suppose that K is a χ-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let λ ≥ Max{χ,LS(K)}. If K is categorical in λ and λ, then K is categorical in λ. Combining this theorem with some results from [Sh 394], we derive a form o...

In a recent paper we gave a counterexample to a longstanding conjecture concerning the characterization of regular languages of level 2 in the Straubing-Thérien concatenation hierarchy of star-free languages. In that paper a new upper bound for the corresponding pseudovariety of monoids was implicitly given. In this paper we show that it is decidable whether a given monoid belongs to the new up...

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption ...

The purpose of the present paper is to show that morphisms between the generic fibers of truncated Barsotti-Tate group schemes over mixed characteristic complete discrete valuation rings with perfect residue fields extend in a “tame-blind” fashion — i.e., under a condition which is unaffected by passing to a tame extension — to morphisms between the original truncated Barsotti-Tate group scheme...